Universita degli Studi di Siena Facolta di Scienze Matematiche Fisiche e Naturali Tesi di Dottorato in Fisica Sperimentale PhD Thesis in Experimental Physics XIX Ciclo

The Legnaro Francium MOT: ecient detection, characterization and perspectives Candidato

Claudio de Mauro

Relatore

Prof. Emilio Mariotti Tutor

Prof. Luigi Moi

From the movie Young Frankenstein by Mel Brooks (1974).

SOSTIENI EMERGENCY

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Contents Ringraziamenti (in italian)

iv

Introduction

1

1 TRAPRAD: production and magneto-optical trapping of francium isotopes

6

1.1 Francium isotopes production . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1.2 The secondary beam line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 The Wien lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 The MOT cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3.1 Time scales in a MOT experiment . . . . . . . . . . . . . . . . . . . . . . 17 1.3.2 Estimate of the characteristic rates . . . . . . . . . . . . . . . . . . . . . . 21 1.3.2.1

Rate W (waste of atoms) . . . . . . . . . . . . . . . . . . . . . . 21

1.3.2.2

Rate L (loading atoms into the MOT) . . . . . . . . . . . . . . . 24

1.3.2.3

Rate C (collisional depopulation of the MOT) . . . . . . . . . . 25

1.4 Neutralisation of ionic beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.4.1 Study of ion implantation and release from catcher foils . . . . . . . . . . 27 1.4.2 Release time measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.4.2.1

Fluorescence of rubidium . . . . . . . . . . . . . . . . . . . . . . 30

1.4.2.2

Rubidium trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.5 The laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2 New detection system for TRAPRAD

37

2.1 Lock-in detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2 Choice of the signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

ii 2.3 Calibration of the signal S . . . . . . . . . . . . . . . . . . 2.3.1 Calibration S $ power . . . . . . . . . . . . . . . 2.3.2 Power emitted by one atom . . . . . . . . . . . . . 2.3.3 Checking the system: the rubidium MOT . . . . . 2.4 Noise analysis . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Weighted subtraction of the background . . . . . . 2.5 First tests with the Rb MOT . . . . . . . . . . . . . . . . 2.5.1 Number of atoms as a function of the laser power . 2.5.2 Reproducibility of the trap position . . . . . . . . 2.5.3 Changing the magnetic eld gradient . . . . . . . .

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3 First results with the Fr MOT 3.1 Trap signal . . . . . . . . . . . . . . . . 3.2 Trap also with cold neutraliser . . . . . 3.3 Di usion time of Fr in yttrium catcher . 3.3.1 Release fraction . . . . . . . . . . 3.3.2 Estimation of trapping eciency

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4 LIAD e ect from dry- lm coating 4.1 4.2 4.3 4.4 4.5

41 41 42 47 48 49 53 54 55 56

LIAD description and signal . . . . . . . . . . . . . . . . . . . . . . . . . . One dimensional di usion model . . . . . . . . . . . . . . . . . . . . . . . OTS dry- lm features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data analysis and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Dependence of the LIAD e ect on the desorbing light wavelength . 4.5.2 Multiple illumination with desorbing light . . . . . . . . . . . . . . 4.5.3 LIAD parameters as a function of intensity . . . . . . . . . . . . . max as a function of intensity . . . . . . . . . . . . . . 4.5.3.1 LIAD 4.5.3.2 Rate R as a function of intensity . . . . . . . . . . . . . . 4.5.3.3 Estimation of eciency . . . . . . . . . . . . . . . . . . . 4.6 Loading of the MOT via LIAD e ect . . . . . . . . . . . . . . . . . . . . . 4.6.1 Pulsed loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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71 72 73 75 76 76 77 79 79 80 80 82 82

CONTENTS

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4.6.1.1 High collisional regime . . . . . . . . . . . . . . . . . . . . . . . 84 4.6.2 Increasing of number of trapped atoms via non alkali desorption . . . . . 86

5 Conclusions and outlook

88

5.1 Energy of the 6D level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 Towards APV measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Bibliography

92

Ringraziamenti La donna che amo e un animale completo, un vertebrato meravigliosamente superiore, idealmente mammifero, decisamente femmina. E, poiche in amore sono nato con la camicia, l'interno ha confermato le promesse dell'esterno... Daniel Pennac in \La Prosivendola" (1989)

Il primo ringraziamento va a chi riesce a capire da dove e tratta la citazione riportata nella prima pagina della tesi, subito prima dell'indice. Per chi non la dovesse capire, spiega bene, secondo me, quelli che sono stati, personalmente, il mio approccio all'esperimento del francio, e, in generale come gruppo di ricerca, i metodi per arrivare ai fantastici risultati descritti in questa tesi. Viene quindi naturale a questo punto menzionare i membri di questa grande collaborazione. Da Siena: il Prof. Moi, il Prof. Mariotti (i quali tra l'altro hanno il coraggio di mettere il loro nome su questa tesi...), Stefano Veronesi (grazie grazie, da te ho imparato molto), Alen Khanbekyan, Alessia Burchianti, Carmen Marinelli; da Pisa: il Prof. Minguzzi e Stefano Sanguinetti; da Ferrara: il Prof. Roberto Calabrese, Sergei Atutov, Luca Tomassetti e Giulio Stancari; da Legnaro: Antonio Dainelli (grazie per lo spumante!) e Lorenzo Corradi. Altri non meno importanti personaggi gravitano al Dipartimento di Fisica a Siena; tutti hanno piu o meno contribuito al mio lavoro qui: Andrea, Simone, Antonino, Vera, Laura, Liliana, Alice, Alessandro, Cesarino, Leonardo, Dani, Valerio, Damiano, Giuseppe, l'allitterato Emilio d'Emilio, Mariella, Roberto, Maria Grazia, Severino e tutti quelli di cui ora non mi viene

Ringraziamenti (in italian)

v

in mente il nome, ma che si sentono di avermi conosciuto in qualche modo. Solo in fondo, ma per dargli un particolare risalto, nomino i frequentatori della stanza dottorandi: Giacomo, Jacopo, Eraldo, Evelina e Claudio...penso che insieme ci siamo anche e soprattutto divertiti. Sempre rimanendo nell'ambito della sica, per un breve periodo all'inizio del dottorato, ho avuto il piacere di poter continuare il lavoro della tesi di laurea sull'esperimento dell'elio a Firenze; per estrema diversita di argomenti non ne puo rimanere traccia in questa tesi, ma cio che ho vissuto e imparato in quel periodo non potro certo dimenticarlo; un sincero grazie quindi anche a Paolo, Pablo, Iacopo, Davide, Giovanni, Valentina, Luigi, Simone e a tutto il personale tecnico e scienti co del LENS. Gli amici di sempre, senesi e orentini, non posso proprio nominarli tutti, altrimenti la lunghezza dei ringraziamenti farebbe sparire quella della tesi...li raggruppo percio in \quelli dell'Osservanza" (grazie per non esservi quasi mai ineressati del mio lavoro, un po' di distrazione ci vuole!!!) e il GruppoSpacca (grazie per aver inventato il Casello!!!). Una menzione speciale la meritano le piccole Maria e Margherita, le ultime arrivate: uno sguardo alle loro fotogra e mi regala un sorriso tutte le mattine. Quasi alla ne ringrazio Pierina, che oltre a farmi nascere mi ha sempre dato il massimo che poteva e anche di piu (con o senza il mio consenso...) e a mio fratello Ciro e mia cognata Annalisa per l'a etto e l'interessamento che mi hanno sempre dimostrato e che spero di contraccambiare sempre anch'io al meglio...a loro una richiesta: guai se uno solo tra Gabriele e Pietro si iscrivera a Fisica. Per quanto riguarda Ele, di parole potrei scriverne tante, l'ispirazione e la fantasia non mi mancano, ma forse nessun discorso, rileggendolo, lo troverei appropriato...quindi prendo in prestito le parole scritte da Pennac, riportate giusto all'inizio di questo capitolo.

Introduction Facts do not cease to exist because they are ignored. Aldous Huxley

The magneto optical trapping of atoms is nowadays a very well consolidated technique to collect a cold, dense and con ned sample of neutral atoms. In the Mendeleev's periodic chart of the elements it is not so easy to nd an atomic species not yet captured in a Magneto Optical Trap (MOT). Since the very original idea of Dalibard [1], the potentials of the method have been developed more and more, up to become commonly used in a very wide eld of applications mainly in atomic physics, but also in other related disciplines. Precision and high resolution spectroscopy, atomic clocks accuracy [2], the way towards the Bose-Einstein Condensation (BEC) [3, 4] received a dramatic push from the development of laser cooling techniques. Trapping of radioactive atoms was obtained in many experiments for studies of fundamental physics, both in atomic and nuclear topics [5, 6, 7, 8]. In particular, alkali atoms, thanks to their ne and hyper ne structure showing at least one circular optical transition directly from the ground state, always represented a very useful tool to implement MOTs experiment and study the features and the behaviour of the atomic species at low temperatures, as well as the physics of trapping itself. Due to the lack of stable isotopes (the longest lived isotope of Fr is the neutron reach 223 Fr with an half life of about 22 minutes), francium atom, the heaviest one of alkali group, has been the last alkali to be trapped in the 90's, by Orozco's group [9], in an on line experiment at the superconducting linear accelerator of Stony

2 Brook (NY). More than a decade after the rst pioneering work of the ISOLDE collaboration at CERN [10], performing the very rst spectroscopic measurement on francium [11, 12], a cold sample allowing more accurate and precise measurements of atomic levels energies [13, 14], hyper ne splittings [15] and lifetimes [16, 17, 18, 19, 20, 21] was obtained. The long term goal of the experiment is the determination of the amplitude of Atomic Parity Violation (APV) (or as also found in literature Parity Non Conservation (PNC)) in atoms [22], which is predicted to be about 18 times greater than in cesium, thanks to Z 3 scaling and enhanced relativistic e ects in a multi-electron system [23, 24]. This fascinating topic represents a demonstration of how low energy physics could be a very powerful approach also to the physics which is usually matter of high energy experiments [25]. In fact, APV amplitude is strictly related to the e ect of the weak interaction between electrons and atomic nucleus, and in particular to the exchange of virtual neutral bosons Z0 : an APV measurements would then be a valid test of the Standard Model of Particles at low transferred momentum. Alkali atoms are especially favourable to measure this e ect because theory of their atomic structure can reach very high precision and accuracy. APV has already been measured in Cs ( rst in Paris [26] and then in Boulder [27]), where the availability of the element doesn't make necessary the implementation of a MOT to achieve a good signal to noise ratio in any spectroscopic experiment. As francium is not naturally available, the only possibility to have a dense enough sample is production at an accelerator facility and on line trapping. In spite of these diculties Fr o ers the interesting possibility of produce and trap di erent isotopes and measure for example the dependence of APV amplitude on the number of neutrons, by varying the weak charge from isotope to isotope. Furthermore the nucleon-nucleon weak interaction, almost inaccessible otherwise, can be studied by searching for anapole moments [28]; the direct study of time-reversal symmetry through detection of permanent electric dipole moments (EDMs) might also be feasible [29]. The experimental setup developed since 2001 at the Laboratori Nazionali di Legnaro (L.N.L.) of the Istituto Nazionale di Fisica Nucleare (I.N.F.N.), substantially follows the one of the Stony Brook facility [30], where an ionic beam of Fr+ ions is produced via nuclear reaction of an 18 O accelerated beam on a gold target, then transported to a glass cell, where it is neutralised and trapped for further studies. Our collaboration TRAPRAD between University of Siena, Pisa, Ferrara and L.N.L.-I.N.F.N. had since the beginning of the experiment a mean beam time of

Introduction

3

14 days per year provided from the TANDEM accelerator facility; after production tests, cross section measurements, transport line implementation [31, 32, 33] and setting up of the optical systems, rst trap signal was seen in 2004, but in the following of the experiment reproducibility of the results was not assured for various reasons. First of all, performances of the accelerator often were not high enough to generate the very high oxygen current necessary to obtain a detectable Fr ux (at the moment our experiment is the one requiring the greater current at the TANDEM accelerator); furthermore, the detection system based on phase sensitive detection had not the sensitivity required to check the presence of a cold cloud of a few tens of atoms, achievable even when the maximum available Fr production is assured. During this thesis work, a complete review of the whole apparatus has been carried out, in order to understand any other possible e ect responsible for failures in detecting the trap signal. We could not use our beam time during more than one year (from May 2006 to June 2007), due to accelerator problems. We took pro t by this forced stop in the online activity, and we carefully checked each part of the experiment (which, as we will see later, is very complicated and sophisticated). In this period, particular care was devoted to the development of a new, very sensitive detection system based on a CCD camera and on subtraction of stray light contribution to noise using a dedicated custom software; the whole apparatus is tested with the Rb MOT implemented in the apparatus itself. In June 2007 we had two days of beam time, but a technical unavoidable problem forced us to give up just before the rst measurement. Finally, on 11th of July, at the very rst laser scan around trap frequency, we saw the trap signal (see g.(1)), with less than 100 210 Fr atoms; in the following two days we were immediately able to improve this result and collect the very preliminary data presented in this dissertation. Also 209 Fr (see g.(1)) was trapped thus demonstrating the feasibility of isotopic e ects studies, by proper choice of the primary oxygen beam energy. At present this represents the only working Fr MOT experiment in the world, while the Stony Brook group is moving at TRIUMF, and another similar experiment is starting in Osaka. As a correlated research activity, in Siena we have developed a Na MOT to study the dynamics of the loading process, in particular related to the source of atoms given by Light Induced Atom Desorption (LIAD) e ect from the cell coating; this loading technique, already demonstrated in the past her positive contribution to the trapping eciency [34]. In particular, during this thesis work, LIAD e ect was for the rst time observed from an OctadecylTrichloroSilane

4

Figure 1: left: about 180 209 Fr atoms trapped and 3D graphical representation; right: about 8000 210 Fr atoms trapped and 3D graphical representation.

(OTS) dry lm coating [35], and also trap loading was obtained. OTS showed a very high desorption eciency, one order of magnitude greater than PolyDiMethylSiloxane (PDMS), the rst compound in which LIAD e ect was observed; Moreover OTS permits better performances in high vacuum environment, as the trapping process requires, making itself the best choice for our purposes. Characterisation of LIAD parameters related to OTS are reported in the dissertation, together with the Rb trap signals. Exporting this method of loading to the Fr trap could be a

Introduction

5

crucial step towards the desirable optimisation of trapping eciency and consequently, towards the measurement of APV signals (together with the rest of measurements) in francium atom.

Chapter 1

TRAPRAD: production and magneto-optical trapping of francium isotopes You need coolin', baby, I'm not foolin', I'm gonna send you back to schoolin', Way down inside honey, you need it... Willie Dixon, Jimmy Page, Robert Plant, John Bonham, John Paul Jones (1969)

Francium atom, the heaviest one of alkali group, o ers a rich variety of possible fundamental studies. First of all, its atomic structure is poorly known; in this perspective, high resolution spectroscopy experiments are opportune, as a possible comparison with theory [36] and previous pioneering works [10]. From a nuclear physics point of view, and decay asymmetries are interesting for the understanding of the deformation of nuclei in heavy radioactive isotopes. Moreover, one of the most fascinating topics is that, due to Z 3 scaling and many electrons enhanced relativistic e ects, Atomic Parity Violation (APV) in Francium atom (from accurate ab initio and many-body perturbative calculations) is predicted to be 18 times larger than in

TRAPRAD: production and magneto-optical trapping of francium isotopes

7

Figure 1.1: general scheme of the traprad experiment; ET - electrostatic triplet, ES - electrostatic steerer, EB electrostatic bender, SSBD - silicon surface barrier detector, WF - Wien lter; each section is separately described in text.

Cesium. APV measurements represent an important test of the Standard Model at low energies, as APV is mainly due to the exchange of virtual Z0 bosons between electrons and nucleons. Francium has not stable isotopes; this represents the main challenge in working with this atom. A Magneto-Optical Trap (MOT) apparatus has been implemented at the INFN National

8 Laboratories of Legnaro (LNL), allowing the collection of a cold sample of Fr atoms, as a rst fundamental step for atomic and nuclear physics experiments on Francium. Our experimental scheme follows the one developed at Stony Brook from Orozco's group; a general scheme of the setup is shown in g.(1.1) and in the following paragraphs each section is described more in detail.

1.1 Francium isotopes production An accelerated ionic beam of 18 O (charge state +6 or +7) with an energy in the range 100120 MeV is provided from the TANDEM accelerator facility; such a beam collides with a thick target of 197 Au. The target is a 8,6 mm diameter disk of 197 Au, with a thickness of about 1mm, and it is placed at one end of a cylindrical tungsten rod as a support. Target is prepared by heating a small amount of 99,99% pure 197 Au placed directly over the tungsten rod kept in vertical position; when the melting temperature of gold is reached a \drop" of gold is \sealed" to the tungsten rod, ensuring a good thermal contact between the two materials. All this procedure is made under vacuum at a pressure lower than 10 6 mbar, to avoid contamination of pure gold from impurities. Once the gold goes back to room temperature, the rod is removed from the vacuum system and mechanically modeled to give to the target a regular shape. Francium isotopes are produced via fusion-evaporation reaction 197 Au +18 O

!215 x Fr + xn

where n represents a neutron and x is an O beam energy for the francium isotopes production, via the integer. In particular we produce all the 197 Au(18 O,xn)215 x Fr reactions. Calculations have been per- Fr isotopes in the mass number range formed with the HIVAP code [37, 38]. 208-211, which have a long enough lifetime allowing for laser cooling; the longest lived isotope in our production range is 210 Fr with Figure 1.2: theoretical cross sections as a function of the

TRAPRAD: production and magneto-optical trapping of francium isotopes

9

an half life of 191 s. According to cross section calculation performed with HIVAP statistical evaporation model [37, 38], the maximum of 210 Fr production rate should occur at an incident beam energy of 91 MeV (see g.(1.2)), and in a range between 80 MeV and 104 MeV; we found experimentally a value of 104 MeV [33]. This is due to the loss of energy of oxygen ion beam into gold target bulk: oxygen beam enters the target at the maximum energy allowing for 210 Fr production and then losing its energy it covers the entire useful range in a thickness of a few m of penetration. To enhance di usion of Fr towards the surface, where it is released and suitable for transport, the system target+rod is resistively heated with a wire wrapped around a ceramic support which surround the tungsten rod and keep the target electrically insulated; temperature is monitored with a commercial pyrometer and is maintained at about 1200K. As already noted by Stony Brook researchers [39], the way to reach the best francium production is to heat the target as close as possible to its melting point. It is possible to reach a very special temperature condition, for which the target is locally melted, in the small irradiated region. This local phase transition manifests itself with a sudden high increase of the francium rate: at the beginning of the transition, a tiny change of the heating power ( PP  10 4 ) resulted in doubling the production rate. When it arrives at the target surface, a francium atom has a signi cant probability to be released in ionic form: according to the Saha-Langmuir equation the ratio between the released ions and neutral atoms is 

n+ g+  I = exp na ga kB T



(1.1)

where n+ and na are the number of desorbed ions and neutral atoms, g+ and ga are the statistical weights due to degeneracy of the ion and atom ground states respectively ( gg+a = 12 for alkalis),  is the surface work function at temperature T , I the atomic ionisation energy, and kB the Boltzmann constant. In our case  = 5; 1 eV, I =4,1 eV [40], then a ratio of the order of  104 is expected. Francium production can be tested and monitored using a silicon surface-barrier detector (SSBD), which is used to reveal the characteristic energies, with a resolution not allowing to completely distinguish between di erent isotopes. The energy of the primary beam can in any case be adjusted to have the maximum production of the chosen isotope. The decay

10 data of the Fr isotopes from A=208 to A=211 are shown in table (1.1), while in g.(1.3) is shown a typical acquired spectrum as a function of the acquisition channels of the detector. Fr 210−211

Counts

Fr 208−209

At204

Channel

Figure 1.3: particles spectrum, emitted from the Fr isotopes implanted on the catcher and measured on a

SSBD; resolution of the detector doesn't allow to separate the four isotopes (A=208-211) mainly produced;204 At lies in the decay chain of 208 Fr and generates the small peak at low energy.

The SSBD is not placed directly along Isotope Half life energy decay the trajectory of Fr ionic beam, but it (s) (MeV) branching ratio detects the particles emitted from ions 208 Fr 59 6,641 90% implanted on an Al catcher, in order to 209 Fr 50 6,646 89% have a well de ned geometry and a mea210 Fr 191 6,543 60% sure of rate independent from the ad211 Fr 186 6,534 > 80% justment of the rst elements of the secondary beam line, which is described in Table 1.1: Nuclear properties of francium isotopes, from A = 208 to A = 211 [41] the next section.

1.2 The secondary beam line After extraction from the gold surface, francium ions are ready to be transported to the MOT cell, about 8 meters away from the scattering production chamber; such physical separation, by concrete thick walls, is necessary to operate in the MOT room in radiation-safe conditions.

TRAPRAD: production and magneto-optical trapping of francium isotopes

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The secondary beam line consists of an extraction electrode (in the scattering chamber near the target), three quadrupole triplets (ET), three steerers (ES), a curved electrode bender (EB) (see g.(1.4)) and a Wien lter (see description in par.(1.2.1)). The extraction electrode, which surrounds the gold end of the tungsten rod, is submitted to a 3 kV voltage (with respect to the scattering chamber, which is kept at ground potential), in order to inject the francium ions into the secondary beam line. The stainless steel electrode is xed on the tungsten rod by means of three screws, therefore achieving the electrical contact with the rod and the target; its conical shape (outer diameter of 69mm and half-aperture angle of 75 ) is designed to minimise the beam divergence and guarantee that all ions are collected, independently of their initial position on the gold surface. The line is set up so that rubidium ions can also be transported. A Rb dispenser was placed inside the target chamber; the release of atoms can be adjusted with the power supply, located in the laser laboratory. Atoms from the vapour which come in contact with the hot gold surface are ionised and accelerated to the same kinetic energy of francium. Rb+ currents of more than 100 nA can be obtained. With this diagnostic tool one can adjust some transport, neutralisation and trapping parameters, even when the primary 18 O beam (and then Fr+ ) is not available. Each triplet consists of three groups of four electrodes (alternately submitted to positive and negative voltages, in the range 70-150 V), mounted on four bars of insulator material (Stesalit); this con guration of electrostatic potentials is an electrostatic lens. The steerer is constituted of two pairs of parallel copper plates, for orbit corrections in the horizontal and vertical planes. The bender is made of two parallel curved aluminium electrodes (actually arcs of a cylinder) operating at 270 V, housed in a case obtained from a single solid block of aluminium. It is possible to easily remove the electrodes and the exit anges, in order to perform alignments by optical means, towards the target on one side, and the MOT on the other side; for this purpose a dedicated optical system and a laser beam from an He-Ne laser has been implemented (see g.(1.4)). Alignment of the gold target support must be carefully adjusted, because even a misalignment of the order of 1 mrad at the beginning of the secondary line can compromise the whole transport eciency. For this purpose a three pivot mount has been installed to ne adjust the tungsten rod axis. A direct monitoring of the francium rate after the passage through the electrostatic elements

12

Figure 1.4: picture of the elements of the electrostatic secondary beam line: ES electrostatic steerer, ET electrostatic quadrupole triplet, EB electrostatic bender; the red line approximatively indicates the optical path of the He-Ne laser beam used for secondary line alignment.

TRAPRAD: production and magneto-optical trapping of francium isotopes

13

is necessary to optimise the values of the applied voltages. To this purpose, four solid-state detectors (SSBD) have been placed along the beam line, in order to count the particles emitted from the francium isotopes. The four SSBD can be inserted in order to intercept the secondary beam, and count the decays of the Fr embedded in them. The voltages of the line elements can be individually changed in order to maximise the francium rate on each detector. The operation is iterated since there is no further improvement on the nal SSBD (the one just before the MOT). This procedure, which takes more than one hour, has to be done whenever the target is changed, because of the unavoidably di erent alignment of the extraction electrode. From run to run (without changing the target), the optimal voltages, which are quickly checked, show an excellent reproducibility, thanks to the good rigid target frame. During one of our shifts, an additional silicon detector was placed inside the MOT cell to check the Fr ux at the position of the neutraliser: we found that about 50% of francium extracted from the target enters the MOT cell.

1.2.1 The Wien lter Before the installation of the Wien lter, when the target was heated and the secondary beam line optimised, we saw a huge thermionic current, mainly due to impurities present in the scattering chamber; in fact the secondary beam line was mass non-sensitive, since the optical elements of the transport line were purely electrostatic: any kind of particle ionised with charge +e from the 3 kV potential of the conical electrode were transported to the MOT cell. A negative e ect on the trapping eciency was observed, as is clearly visible in g.(1.5). When this thermionic current, whose intensity strongly depends on the target temperature, enters the MOT cell, the number trapped atoms suddenly decreases and the signal level is fully restored when the thermionic current is stopped again. The characteristic time of decay of the signal is slightly shorter than the characteristic rise time measured from the signal in g.(1.5); this is probably an indication that such a huge thermionic current in uences mainly the vacuum conditions in the MOT cell. In fact the current is prevented from reaching the cell without changing the work conditions of the vacuum system (all valves always remain open), but turning o one of the electrostatic elements of the secondary beam line (usually the electrostatic bender). Since we are interested in only one isotope at a time (Rb+ when checking the system or Fr+ during beam time) the solution we implemented to overcome this problem was to install

14

Figure 1.5: Rb trap signal (upper curve) and thermionic current (lower curve) vs time. The horizontal scale is

5 s per division. At t=5 s, the magnetic eld was turned o for 3 s in order to show the background level due to stray light; coorelation between thermionic current and trap signal depletion is evident.

a Wien lter in the transport line. This device produces a magneto-static homogeneous eld B~ via an electromagnet, perpendicular to an electro-static homogeneous eld E~ generated from to parallel metallic plates. A particle entering the lter with charge q and velocity ~v is subject to a force given by the well known Lorentz formula F~ = q(E~ + ~v ^ B~ ) E If the velocity satis es the condition v = , the particle is not de ected from the two crossed B elds: the Wien lter is then in principle a velocity selection device. In our ionic beam the energy is xed from the extraction electrod potential to  =3 keV, hence

1 2 Mv = q =) v = 2

r

2q M

TRAPRAD: production and magneto-optical trapping of francium isotopes



15



85−87 







Figure 1.6: mass spectrum of the thermionic current; Rb+ peak is used for calibration and obtained from a Rb dispenser heated in the scattering chamber; the other two peaks correspond to the mass of K and Na.

If we only consider particles singly ionised, the velocity Wien lter acts as a mass separator. A typical mass spectrum obtained at a xed current in the electromagnet (the value of the 0; 29T magnetic eld is given by the formula B = I where I is the current measured in A) while 14A scanning the electric eld by changing the potential between the two plates is shown in g.(1.6). A beam of Rb+ is sent through the line from a Rb dispenser heated in the scattering chamber in order to obtain mass calibration of the spectra; the current is measured by a picoammeter connected to the neutraliser placed in the MOT cell. An estimation of the mass resolution of the lter is given by M  4s = M dLE where d is the drift distance from the lter center to the beam detector (the neutraliser in

16 the MOT cell in our case, so d ' 3; 5m), L is the length of the lter itself (L = 15; 2cm), s represents the transverse typical dimension of the beam detector (s ' 1cm) and E is the value of the electric eld in the lter; this formula is valid in the approximation d  L and for a point M like transverse pro le of the ionic beam. As we can see resolution increases (i.e. the ratio M decreases) proportionally to the value of the electric eld; once velocity is xed this means that the greater is the magnetic eld, the greater is the resolution. If we work at a current of about 8 A, which is the maximum value allowing the passage of both Fr and Rb only by changing the electric eld (a maximum voltage of 150 V can be applied to the lter plates), we obtain for M Rb an estimate of the resolution of ' 0; 017. M M From the acquired spectra we measure instead ' 0; 12. This is not surprising because from M lter to cell there is not a simple drift of the beam, but also an electrostatic bender and a triplet; moreover the nite size of the beam transverse pro le worsens further the resolution. For Fr ions this corresponds to a M ' 25, so no other alkalis enter the cell when lter is running. This clearly means that we are not able to select the contribution to the total ux of the di erent Fr isotopes.

1.3 The MOT cell The cell is a standard Pyrex glass spherical balloon; its radius is about 7 cm and hence with a volume of about 1500 cm3 . The connection with the high vacuum system is obtained with a glass-metal high-vacuum connection (12 cm long and 2.5 cm in diameter). Six plane Pyrex windows of 4 cm diameter are sealed on three orthogonal directions to allow the passage of MOT laser laser beams; anti-re ection coating is not used. On one side a smaller window (1,4 cm in diameter) is placed to have a better optical access for trap detection. In diametrically opposed position we sealed a glass-metal high vacuum connection of 1 cm diameter; this is very useful mainly for two reasons: rst of all we can connect an alkali reservoir (potassium, rubidium and sodium were used) to make a curing of the cell coating, furthermore we obtain a strong reduction of the scattered light entering the detection system from the small window by using a Wood horn. A quadrupolar magnetic eld is produced at the center of the cell by two anti-Helmholtz coils, placed collinearly to two of the six optical windows.

TRAPRAD: production and magneto-optical trapping of francium isotopes

17

Inner walls of the cell are coated to reduce atom sticking; organic compounds as PDMS and OTS dry lm were used and we found that with OTS (or any other kind of dry lm) we obtain better vacuum conditions with respect to PDMS: in fact, after few weeks pumping, we measure a lifetime of the Rb trap of about 5 s, while with PDMS after two months pumping, such a time is at least a factor of two worse. To better understand the importance of the cell construction and geometry in a magnetooptical trapping experiment, we will analyse in the next paragraph, how these features in uence the number of trapped atoms and the trapping eciency.

1.3.1 Time scales in a MOT experiment The total number of atoms in the cell, when the six laser beams and the magnetic eld are present, is the sum of two contributions: the number of trapped atoms Nt and the number of atoms in the vapour phase Nv which is supposed to be at thermal equilibrium at the temperature of the cell walls. The time evolution of Nt and Nv is well described from the coupled rate equations [34] 8 > <

N_ t = LNv

> : N_ v

=

CNt

BNt2

ANv Nt

r Nt

(L + W )Nv + CNt + BNt2 + ANv Nt

r Nv

+f

(1.2)

At this point it is useful to summarise the physical meaning of the terms in equations (1.2), further explanation will be given later when necessary

 L is the rate related to the loading process and the product LNv represents the number of atoms per unit time loaded from vapour in the MOT; a theoretical model discussing the dependence of L from parameters such as mean thermal velocity of non trapped atoms and gaussian radius of laser beams can be found in [42]



C is the rate describing the collisional loss of atoms from the MOT to the vapour phase

and the product CNt represents the number of trapped atoms per unit time which go back from trap to vapour phase due to collision with background gas in the cell, so C increases with the pressure in the cell



BNt2 and ANv Nt are also collisional terms, acting in depopulating the trap: the rst one is

the cold collisions rate while the second one takes into account collisions between trapped

18 and non-trapped atoms; this two terms are often negligible and become signi cant (or even dominant with respect to other terms) for example when a huge amount of atoms is suddenly released in the cell; if not else stated, we will consider in the following A = B = 0



W is the rate characterising the loss of atoms from the vapour phase and the product W Nv

represents the number of atoms per unit time de nitively lost; loosing of atoms can occur for example through the cell aperture towards the pumping system or through sticking on to the cell walls



is the reciprocal of the radioactive lifetime of the considered atoms ( r = 0 for stable atoms as 85 Rb); the rate equations (1.2) don't constitute a closed system due to this term and the previous one W , hence a source of atoms is needed which is given by the last term r

 f is the current of atoms entering the cell from a generic source: this can be realized by a reservoir directly connected to the cell (if available, for Fr isotopes this is not the case), by releasing of atoms embedded in the coating of the cell (as we will see later) or with the neutralisation of an incoming ionic beam All this terms, but r , are in general function of time; all this time dependencies make the solution of the system of equations (1.2) not so trivial if no assumption is made. As a very rst consideration we can nd the stationary state solution N_ t = N_ v = 0 under the condition f_  W; L; C , i.e. slowly varying incoming current hypothesis f 8 L > > Nt = f < (W + r )(C + r ) + L r (1.3) C+ r > > : Nv = f (W + r )(C + r ) + L r Solution (1.3) reduces for stable isotopes to Nt =

Lf WC

Nv =

f W

(1.4)

In order to have an analytical solution for Nv (t) and (much more important) Nt (t) the simplest situation is to consider a stable isotope and all the rates L; C; W and the current  as constant terms; if written in vectorial form, the matrix associated to the system is 0

K=@

C C

L

1 A

(L + W )

TRAPRAD: production and magneto-optical trapping of francium isotopes

19

Na Trap Signal (a.u.)

150

100

50

0 10

5

15

20

Time (s) Figure 1.7: sodium MOT signal and t curve (in red) with double exponential, following eq.(1.4) for Nt (t); at t '1 s the magnetic eld is turned on, triggering the loading process; results of t are k1 = (1; 4  0; 4) s 1 and k2 = (0; 53  0; 15) s 1 .

so the solutions of the homogeneous system will be a linear combination of exponential terms with time constant given from the eigenvalues of K, and particular solution are (1.4) 8 > <

Lf WC (1.5) > : N (t) = a e k1 t + a e k2 t + f v 3 4 W the set of constants ai is properly determined once assigned the initial conditions Nt (0) and Nt (t) = a1 e

k1 t + a

2e

k2 t +

Nv (0). An example of this kind of signal is reported in g.(1.7), where we show the time evolution

up to the steady state condition, of the population of a 23 Na MOT (a spectacular picture of the MOT is shown in g.(1.8)), developed at the Department of Physics in Siena during my thesis work; this experiment is developed in parallel to TRAPRAD to study trapping eciency on stable isotopes and eventually to apply the measured improvements to Fr MOT. Trapping laser

20

Figure 1.8: picture of the Na MOT cell in Siena; trap is clearly visible by eye from the uorescence at 589,6 nm; trapping laser is a Coherent 699 dye laser tuned on D2 line, while repumping is obtained from the main laser sidebands generated in an EOM at 1,712 GHz.

is a Coherent 699 dye laser tuned on D2 line at 589,6 nm, while repumping is obtained from the main laser sidebands generated in an EOM at 1,712 GHz; cell geometry and laser beam radius are very similar to those of Legnaro experiment; sodium atoms are stored in metallic form in a reservoir sealed to the cell and Na vapour pressure is increased by resistively heating, up to 80 C, the reservoir itself. Fit curve with the double exponential function is shown in red and the model is con rmed to be adequate to describe the trapping process obtained by turning on the magnetic eld at t '1 s; this corresponds to an initial condition of Nt = 0. Results of t for the two time constants are k1 = (1; 4  0; 4) s 1 and k2 = (0; 53  0; 15) s 1 .

TRAPRAD: production and magneto-optical trapping of francium isotopes

21

Finally we write the expressions for k1 and k2 as functions of W , L and C 8 > < k1

p 1 C + L + W + (C + L + W )2 2 p 1 > : k2 = C +L+W (C + L + W )2 2

=

4CW 4CW

 

(1.6)

1.3.2 Estimate of the characteristic rates A possible way to estimate these time coecients, independently from trap evolution is explained in the next paragraphs, where we also de ne another important parameter: the trapping eciency.

1.3.2.1 Rate W (waste of atoms) In a simple description we could think to the evolution of the atom number Nv inside the cell in terms of a rate equation, where the source is given from the incoming atomic current f and, under the hypothesis of a perfect coating (probability for an atom to stick on the cell walls equal to zero), the loss is given by the di usion through the connection tube towards the vacuum 3Nv ~ nj. system: the outgoing current in terms of atom density n = can be written as DK jr 4R3 ~ nj ' n , where The gradient of density is evaluated in the tube and can be approximated with jr L 2rvT L is the length of the connection tube, R is the radius of the cell and DK = is the di usion 3 r 8kB T is the mean thermal velocity of atoms. coecient in the Knudsen regime and vT = M Finally we obtain N_ v = f

W Nv = f

 r2DK L

 r 3

3Nv =f 4  R3

R

vT N 2L v

(1.7)

where r is the radius of the aperture of the cell. The waste coecient W (in the following 1=W is also named escaping time) is then given from W=

 r 3

R

vT 2L

With our numbers for Rb and Fr WRb ' 26 s

1

WF r ' 16 s

1

For the sake of completeness we have to do some consideration about this result: rst of all, these estimates only represent a lower limit for W , because we haven't considered other losses

22

Figure 1.9: escaping time 1=W measured as a function of the laser frequency; origin in the frequency axis is xed with the maximum MOT signal;time is measured from t of the exponential decay of uorescence from atoms in the cell after opening a Rb reservoir for a short time ( 100 ms).

of atoms but the cell aperture; non-coated part as Wood horn or the neutraliser feedthrough have an in uence on the waste of atoms. Another e ect to take into account is that even with magnetic eld o a mechanical e ect of light on the atoms is present and, by slowing the atoms, has a signi cant e ect on W depending also on the laser frequency (see g.(1.9)): this is the famous and well experimentally and theoretically studied [43, 44] optical molasses e ect, which even could allow to reach lower temperatures than a magneto optical trap, as demonstrated in [45]. The measurement shown here are performed using a photodiode close to the cell, initially supposed with no Rb in the vapour phase, which detects the uorescence of Rb atoms in presence of both trapping and repumping lasers. While repump laser is maintained at resonance, di erent measurements are made scanning the trap laser frequency for a few tens of MHz across the position where trap signal is optimised. A Rb reservoir connected to the

TRAPRAD: production and magneto-optical trapping of francium isotopes

23

Figure 1.10: acquired signal and t curve (in red) of the uorescence of Rb atoms obtained by opening of a reservoir connected to the mot cell for a time of a few hundreds of ms.

cell through a valve: if the valve is open for a short time interval (typically few hundreds of ms), uorescence signal exponentially grows because of Rb atoms di use into the cell and when the valve is closed starts to exponentially decrease with the same time constant. Such a time constant is hence a measure of the escaping time of atoms from the cell. We t the obtained signal with a model function taking into account both the growing and the decaying part of the signal, leaving as free parameters the valve opening time, an amplitude factor and the more interesting escaping time 1=W . A typical signal with its t curve is shown in g.(1.10). Results for di erent laser detunings are shown with error bars given from the ts. The trend of the data seems to show a peak which is higher by a factor of two than a plateau observed at other laser

24 detunings, when only free di usion contributes to escaping of atoms and dissipative forces due to laser beams become less e ective. To our knowledge, no mention on this e ect is made in literature when evaluating the coecient W to determine for example the trapping eciency (see de nition below) in a MOT experiment. For example in [46] W is measured from uorescence induced from a weak laser beam through the cell, but this is not the situation experienced from the atoms when all six MOT beams are present. More accurate studies are anyway necessary to understand if this e ect can be used to help in some way the trapping process. Furthermore, the assumption of a sticking probability equal to zero due to a perfect coating is clearly optimistic: adsorption of atoms in the coating is observed because we are able to observe the opposite process of desorption from the coating itself. In fact a huge number of atoms can be stored in the coating, as observed in many LIAD experiments; reaching an equilibrium situation requires at least three weeks of pumping to saturate the coating. Due to this last consideration, a more accurate model have to take into account at least surface e ects at the vapour-coating interface, adding a loss term in eq.(1.7) fcoat =

3 vT pst 3  vT  R2 Nv pst = N 3 4R v 4  R

1 where pst = is the probability of sticking, inversely proportional to the mean < nbounces > +1 number of bounces on to the cell walls an atom can do before sticking; therefore we obtain W = vT



2  r 3 3pst + L R 4R



At this point one could think that there's no reason to not construct a cell as big as possible in order to decrease W . Actually this is not a good idea for many reasons: rst of all a bigger cell requires a longer time to get steady state in atom density when lled from an external source; furthermore for a given size of the MOT laser beams the ratio between the trapping volume and the total volume decrease with increasing R, giving a lower loading coecient.

1.3.2.2 Rate L (loading atoms into the MOT) According to ref. [42] an expression for L could be L=

1 vc 3  w p = R 3 4  v 4  R3 4

T



2

3

TRAPRAD: production and magneto-optical trapping of francium isotopes

25

where w is the gaussian radius of the laser beams and vc is the capture velocity, de ned as the maximum velocity an atom must have to be trapped in the shallow magneto optical potential. As well discussed in [47] calculation of vc is not straightforward, and very accurate numerical simulation is required; what is found is that vc primarily depends on intensity and area of MOT beams, but no analytical expression is given apart of an order of magnitude which is vc   where is the natural linewidth in rad s 1 and  the wavelength of the trapping transition vcRb  vcF r  30ms

1

As we use the same optical system for Rb and Fr, we have in both cases w '1 cm, and hence the di erence between Rb and Fr lies only in the mean thermal velocity, so we obtain LRb ' 1; 2  10

3

s

1

LF r ' 4; 8  10

3

s

1

From L and W we can de ne the trapping eciency as the ratio =

L L+W

which represents the fraction of atoms per unit of time which are trapped and not lost after leaving the vapour phase. We have, for the above calculations =

R

R h

3

i  3 + vT 2 r 3 + 3pst L R 4R

=

 + vT

h

 i 2 r3 + 3pst R2 L 4

This is another good reason to not increase too much the size of the cell: in spite of a longer escaping time of atoms, for an actual not ideal coating (pst 6= 0), the trapping eciency decreases as the square of R.

1.3.2.3 Rate C (collisional depopulation of the MOT) As already stated before, the collisional coecient C taking into account trap losses due to background gas, strongly depends on pressure. An estimate can be given by C = P vT 3; 3  1016 torr 1 cm

3

where  is the cross section in cm2 , P the pressure in torr and the mean thermal velocity is measured in cm s 1 . We are not able to measure the product vT , but an order of magnitude for C could be a few 10 1 s 1 (by modelling the atom as a rigid sphere of radius  250 pm, by

26 considering a thermal velocity of 250 ms 1 and with a typical maximum pressure of 510 8 torr). As we expect L  W , from equations (1.6), it is easy to deduce that k1 ' W and k2 ' C ; furthermore it is always true that k1 > k2 , so one of the two exponential terms in Nt (t) vanishes more rapidly than the other one. This implies that a measure of the time interval from the beginning of the loading process (for example, turning on at t = 0 the coils magnetic eld when the atomic density in the cell gets steady state) to the instant when the trap signal reaches the 70% of the steady state value, gives a good estimate of C 1 . We usually measure an increase of this time interval from 1 s to more than 5 s during a couple of months pumping of the cell and a consequent increase in the trap population, as expected. At this point it is worth to remark the crucial importance of a good vacuum system for a MOT experiment.

1.4 Neutralisation of ionic beam When an ion joins the MOT cell we have to make it suitable for magneto optical trapping, i.e. it must be neutralised. We then focus the ionic beam on a yttrium catcher, placed inside the cell on the opposite side with respect of the entrance aperture. Yttrium has a work function of 3,1 eV, lower than ionisation potential of Fr atom of 4,01 eV; according to Saha-Langmuir's equation (1.1) the probability for a Fr atom to be desorbed from Y surface in atomic form rather than as an ion is increased due to this characteristic. Moreover melting point of yttrium is 1526  C, allowing us to maintain the neutraliser foil at high temperature to enhance di usion towards the surface. We choose not to exceed 750  C in order to avoid a thermal damage of the cell coating. The Y foil is 25 m thick and about 11 mm10 mm wide; it is mechanically xed to molybdenum legs in electrical contact; such legs are then connected to an high vacuum two pin electrical feedthrough, so that a DC current up to several Amps can be injected in the neutraliser for thermoelectric heating. One of the electrodes is grounded to avoid charging of the region surrounding the yttrium from the ionic beam. Once the neutraliser is installed inside the cell we measure its temperature as a function of the electric power provided from the current generator; temperature is measured from outside the cell using a commercial pyrometer, whose calibration was veri ed at the melting point of yttrium; the typical curve temperature versus power is shown in g.(1.11).

TRAPRAD: production and magneto-optical trapping of francium isotopes

27

Neutralizer surface temperture (°C)

This construction is mechanically not so strong, because of af700 ter a few weeks of heating under vacuum, mechanical stresses on 600 the yttrium foil due to high working temperature may cause 500 fractures and hence breaking of the foil itself; for this reasons 10 20 30 Electrical Power (W) we are at the moment Figure 1.11: temperature vs electrical power for yttrium foil used as ionic beam planning to change neutraliser; temperature is measured from outside the cell using a commercial pyrom- construction to make eter, calibrated at the melting point of Y (1526  C). it more resistant, for example by melting of a small amount of yttrium under vacuum just over a tantalum (easier to shape as molybdenum) support, following the nal design used in [48], suitable for the installation inside the cell.

1.4.1 Study of ion implantation and release from catcher foils In many experiments dedicated to the study of the properties of radioactive atoms, elements are produced in ionic form and then neutralised as in our experimental setup. The most important feature required to a neutralisation system is the fast release of radioactive neutral atoms if compared with the lifetime of the nucleus. Once an ion with an energy of the order of a few keV bombards the surface of a metallic material, a rich variety of processes could take place due to elastic (sputtering, ion scattering) or inelastic (x-rays and optical photons emission, secondary electrons) collisions [49], with probabilities depending on the energy and mass of the ion and on the crystalline structure and mass of the metal catcher. If the ion is implanted in the catcher at some depth from its surface, then it has to di use towards the surface and here released in neutral form. In this description, such di usion time has to be small compared with the

28 radioactive lifetime of the investigated atom. To give an estimate of the order of magnitude, a di usion model gives, for this di usion time d2 d = 4D where d is the mean implantation depth of ions in the catcher foil, and D is the di usion coecient; empirically one can be nd a dependence of D from the temperature following an Arrhenius law   Ea D = D1 exp kB T where Ea is the activation energy and D1 is the asymptotic value of D in the physically meaningless limit T ! 1. From this formula it is easy to see how high temperature enhances di usion. For radioactive isotopes with lifetime rad = r 1 , the one dimensional di usion equation in a thin catcher can be written as @ 2 N (x; t) @N (x; t) =D r N (x; t) + '(x; t) @t @x2 where N is the concentration of atom in the catcher and ' is the incoming current of ions (in ions/cm 3 s 1 ) impinging on the catcher. Under the simplifying hypothesis that N0 ions are implanted at the same distance d from the surface and at the same time t = 0, analytical solution of the di usion equation for the concentration of ions in the material with '(x; t)  0, gives a ux of neutral atoms released in the cell at time t [50]   d2 N d t 3=2 F0 (t) = p 0 p exp exp ( r t) (1.8) 4Dt 4 D In case of an implantation distribution with a nite extent a correction factor depending on the width of the distribution should be taken into account, but it can be shown that such a factor is close to unity in the case that r  d 1 . In our experiment we send a current of ions on the neutraliser (whose intensity I (t) = R '(x; t)dV is the integral over the neutraliser volume of '(x; t) and is then measured in ions/seconds) can be in some way time dependent. In this case the ux of neutral atoms F (t) released in the cell is then given from the time convolution of I (t) and 0 N0 Z t 0 F (t t ) 0 F (t) = I (t0 ) 0 dt N0 0

TRAPRAD: production and magneto-optical trapping of francium isotopes

Incoming current I0 Neutral current F(t) Neutral "pulsed" current F0(t-20s)

1

Current (a.u.)

29

0,5

0 0

20

40

Time (s) Figure 1.12: time trend of the ux of neutral atoms released from a catcher foil; all uxes are normalised to I0 ; di usion time d is set to 1 s and toff = 20 s.

For our purposes it is interesting to calculate what happens when I (t) suddenly raises, at t = 0, from 0 to a certain constant value I0 and goes back to zero after a time toff . For stable isotopes, i.e. r = 0

F (t) =

8 > > > > > > > <



0

I0 1 erf

> >  r > > > > > : I0 erf

r

d t toff



d t

for t < 0



erf

r

for 0  t  toff d t



(1.9)

for t > toff

An example plot of F0 (t) and F (t) for a step shaped I (t) is shown in g.(1.12). For unstable isotopes there is no analytical solution for the time convolution integral, but under the condition 1 1 r  d ; toff , the exponential decay factor exp ( r t) can be considered approximately con-

30 stant and hence it multiply the above expression for F (t); in any other case, numerical solution of the di usion equation inside the catcher can be performed.

1.4.2 Release time measurements 1.4.2.1 Fluorescence of rubidium When the Y foil is heated up to 500  C, we are able to observe uorescence of Rb atoms, even without an external Rb source, probably because Rb is an impurity in Y foils. To test the eciency of our neutralisation system we choose to measure the variation of the uorescence signal from Rb atoms, when an ionic beam of Rb is sent in the cell from a source placed in the scattering chamber. In such an experiment, density is too low to observe directly the uorescence light with a photodiode, so we modulate the repumping laser (see next section for a description of laser systems) at a frequency of 10 kHz and perform a phase sensitive detection. The typical observed signal obtained by scanning the main laser is shown in g.(1.13). We set the frequency of the lasers at the maximum 6 of this signal, in order to have the 4 best sensitivity. We measured the ef2 fect of ionic beam on the uorescence for di erent tem0 -800 -400 0 400 peratures of the Frequency (MHz) neutraliser, and we Figure 1.13: uorescence signal from Rb atoms in the cell while scanning main laser conclude that no frequency across the resonance of the D2 line starting from the F = 3 ground state; zero e ect is visible in frequency is arbitrarily xed at the maximum of the signal; Doppler broadening is not a time interval of resolved. 300 s for tempera-

Lock-in signal (µv)

8

TRAPRAD: production and magneto-optical trapping of francium isotopes

31

ture lower than 550  C. For temperatures in the range from 620  C to 720  C we are able to t the acquired signals with the function given in eq.(1.9); on the left side of g.(1.14) an example of signal and t curve is plotted, while on the right side of the gure di usion time as a function of temperature is shown; it should be evident that our data are consistent with Arrhenius law for the di usion coecient D. We t data with the function d = 950





E 1 exp a kB T

1 950K



(1.10)

where 950 is the di usion time at 950 K; t parameters are both the time 950 and the activation energy Ea : results of t are 950 = (21  5) s and Ea = (1; 8  0; 3) eV. An activation energy of Ea = (1; 59  0; 15) eV was measured for yttrium in [51], so our result is consistent with the previous one; using the TRIM code [52] to have an estimate of the mean implantation depth d of 85 Rb ions incident on Y at 3 keV energy, we can then calculate the di usion coecient for 85 Rb in Y at 950 K d = 49 A d2 D950 = = (2; 8  0; 6)  10 15 cm2 s 1 4950 To make a meaningful comparison with the data measured in [51] we can evaluate the parameter D1 , which has to be independent on the di using ion 



E 1 = 1; 0+60;;59  10 D1 = D950 exp a kB 950K

5

cm2 s

1

This result is consistent mainly because of the big asymmetrical error bars due to the fact that we propagate errors from nite temperature to the physically meaningless limit of in nite temperature.

1.4.2.2 Rubidium trap We also studied the e ect of the ionic beam and the eciency of the yttrium neutraliser on the number of trapped atoms. As previously discussed the trap population depends on many parameters (vacuum conditions, laser frequency, good de nition of circular polarisation of laser beams in the cell,...), making not easy a comparison between measurement performed at di erent times. In order to predict time evolution of the signal (acquired with the CCD based system which will be described in chapter 2), we have to combine the di usion equation of Rb atoms

100

8

Characteristic release time (s)

Fluorescence signal variation (a.u.)

32

6 ionic beam on 4

2

0 0

50

100

150

Time (s)

200

250

300

80

60

40

20

0

900

920

940

960

980

Neutralizer temperature (K)

Figure 1.14: on the left: uorescence signal from neutralised ions (black curve) and t curve from eq.(1.9) (in

red) at a temperature of 680  C; on the right: di usion time as a function of temperature (error bars are given from t); blue curve is a t of the data with the function given in eq.(1.10).

in the catcher bulk, with the coupled equations (1.2) of time evolution of number of atoms in the vapour phase and number of trapped atoms, already described in paragraph 1.3.1. In particular, the source term f has to be given from the neutral current released from neutralised and calculated from di usion equation. Here we suppose that released atoms in the vapour phase instantaneously di use in the cell volume so the density in the cell could be considered as position independent. For this purpose we developed a simple code in the Octave [53] platform, in which the di erential di usion equations are numerically integrated following a simpli ed version of an algorithm developed and discussed to describe LIAD from siloxane coatings [54]. In g.(1.15), we show the increase in the trap population (with respect to the \background trap" due to Rb vapour coming from neutraliser heated up to 700  C) when Rb ionic beam is sent in the cell, and the corresponding decreasing when beam is interrupted. For comparison a simulation of the experiment is shown: it is evident that experimental data and calculation are consistent. The parameters used in the simulation for the di usion are also consistent, at least as an order of magnitude, with the measured ones. The small disagreement at the end of the measurement was due to frequency shift of repumping laser. We measured a current of about 8 pA on the neutraliser with a commercial picoammeter, with a corresponding variation in the number of trapped atoms of .600; it is anyway not so useful to calculate a conversion factor between ionic current and number of trapped atoms, because of current measurement is a ected from unpredictable systematic e ects, such as secondary electrons emission or di erent

TRAPRAD: production and magneto-optical trapping of francium isotopes

33

ionic beam off

600

∆Nt

400

200 ionic beam on

0 0

50

100

150

200

250

Time (s) Figure 1.15: black curve: variation of number of trapped atoms as a function of time when ionic beam is sent on

the neutraliser and stopped by misalignment of the secondary beam line. The temperature of Y foil is 700  C; green curve: theoretical curve calculated by numerical integration of di usion and trapping equations; inconsistencies in the nal part of the plot are due to accidental frequency shift of the repump diode laser frequency.

backscattering coecient from Y for the two natural Rb isotopes 85 and 87. Moreover this systematic e ects act di erently on Fr beam, so we can only evaluate an order of magnitude for the expected signal for Fr trap. What is crucial for our purposes is that we observe a proportionality between measured current and corresponding trapped atoms, and a characteristic time of formation of the trap much shorter than 210 Fr and 209 Fr lifetimes. If we simply apply a proportionality relation, we predict a signal of about 20 atoms with a current of 106 ions s 1 , which, as we will see later, is an underestimate of the observed signal. This is explained from the fact that in the same conditions Fr atoms are heavier and then slower than Rb atoms at the same temperature, so trapping process is easier.

34

1.5 The laser system For our experiment we need at least four di erent laser frequencies to have the possibility of trap both Fr and Rb, i.e. trapping and repumping transition for each one. An outline of the optical scheme is shown in g.(1.16). A Coherent 899 Ti:Sapphire laser pumped with an Innova Sabre Ar+ laser (also from Coherent Inc.) allows us to reach the pumping transitions of both atoms (780 nm for Rb and 718 nm for Fr) with a total laser power (adjustable via the pump laser power) greater than 500 mW and with an extra-cavity Fabry-Perot system for frequency stabilisation. In the path from the laser to the MOT cell, plced about 5 m apart, a beam splitter plate separates two weak beams from the Ti:Sa light: one of them is sent to a Burleygh WA-1500 wavemeter for wavelength measurement (we use an optical ber input to get the better accuracy and reproducibility with respect to the alignment of the laser beams), the other one is sent to a high nesse Fabry-Perot cavity to monitor the spectral quality and frequency jitter of the laser using the sharp transmission peaks. Switching from Fr to Rb wavelength is achieved by rotation of an intra-cavity Lyot birefringent lter and a consequent slight realignment of the whole laser cavity to restore optimal output power. Two diaphragms xed on the laser beam optical path ensure also the optimal restoring of the alignment of the beams until the MOT cell. A system of beam splitters properly divide the total power into two \strong" beams with double intensity with respect to the other four \weak" beams. Each beam before entering the cell passes through a quarter-wave plate to obtain the proper circular polarisation and then a 20 magnifying telescope to maximise trapping volume and then the loading rate. Polarisation and ellipticity are monitored just before the cell windows using a home made device in which a linear polariser rotates thanks to a mechanical gear and a photodiode detect the transmitted light. Rotation and tilting of quarter-wave plates allows us to obtain a constant signal (circular polarisation) for both Rb and Fr wavelengths; if polarisations of trapping beams are not well de ned we observe a greater instability in the trap signal and position, which can be very e ective in detection of a trap of less than 1000 atoms. Repumping requires less power and is achieved using two diode lasers; for Rb we use as repumping transition another component of the D2 line at 780 nm, while for Fr we repump via the D1 line at 817 nm. Light from diode is superimposed to the optical path of the Ti:Sa laser

TRAPRAD: production and magneto-optical trapping of francium isotopes

35

Figure 1.16: outline of the optical scheme for trapping and repumping; repump diode laser (DL) is selected from Rb and Fr using a ipping mirror (not shown); QPW - quarter wave plates, BE - beam expander, FP Fabry-Perot cavity used for active stabilisation of diode lasers; stabilised He-Ne laser is used as a reference for the stabilisation of the cavity; optical ber input to the wave meter is used, to ensure reproducibility of the wavelength measure, independently on alignment.

Photodiode signal (a.u.)

36

DL spectrum He-Ne spectrum cavity FSR

a

Frequency Figure 1.17: typical signal from the photodiode after the Fabry-Perot cavity of the laser stabilisation system; stabilised He-Ne transmission peaks are used as a reference for the cavity length, adjusted via a piezo actuator mounted onto one curved mirror; a software controlled algorithm keeps constant the distance a from the diode peak to one of the He-Ne peaks, closing a feedback loop on the diode current.

and a ipping mirror is used to send alternatively towards the MOT cell the proper beam. For both lasers we can perform wavelength measurement with the Burleigh wavemeter and the Fr repumping is actively stabilised with respect to an He-Ne lasers through the transmission peaks from a Fabry-Perot cavity [55]. Stabilised He-Ne transmission peaks are used as a reference for the cavity length, adjusted via a piezo actuator mounted onto one curved mirror; a software controlled algorithm keeps constant the distance \a" from the diode peak to one of the He-Ne peaks, closing a feedback loop on the diode current; a typical signal used for stabilisation is shown in g.(1.17).

Chapter 2

New detection system for TRAPRAD You don't have to worry long, long as I can see the light. J.C. Fogerty (1970)

Even working in the best condition of vacuum, neutralisation eciency, MOT cell construction, etc. we can estimate that with the ux of Fr ions provided by the tandem accelerator at LNL, we are able to trap few thousands of Fr atoms. Obviously we don't live in an ideal world, so we could have to treat and detect a cold cloud containing only few hundreds of atoms, before a complete optimisation of all the trap parameters (laser frequencies and intensities, magnetic eld gradient, vacuum conditions in the MOT cell, etc.); this means that we need a detection system very sensitive and with low noise.

2.1 Lock-in detection A classical technique to extract a small signal from a noisy environment is phase sensitive detection via a lock-in ampli er. At the beginning of the experiment, the heart of the detection

38 system was a photodiode with a proper optical system which formed an image of the trap in the plane of the photodiode, giving an electrical signal proportional to the power emitted by cold atoms. The idea of lock-in detection is to introduce a modulation in the trap signal or to use an intrinsic frequency component of the signal itself. This can be done in di erent ways; here we summarise the test we made with stable Rb trap with di erent modulation techniques and the problems faced with each technique.

Modulation of magnetic eld: a third coil, placed in an orthogonal plane with respect to the antiHelmholtz coils of the main trapping eld, can provide a slow (Hz or sub-Hz frequency) uctuation in the position of the cloud; for an intense stable Rb trap we observed with this technique a loss of S/N ratio; furthermore this freFigure 2.1: noise spectrum of the trap signal acquired with a photoquency region of the spectrum is diode; harmonics of the line frequency (50Hz) are clearly visible. not favourable to improve this situation as we can see in g.(2.1).

Chopping of trap or repump laser: a mechanical chopper can be placed both in the optical path of trapping and repumping laser, in order to choice an higher modulation frequency in a region where the noise spectrum is lower (more than 200Hz for example): this leads to a huge loss in the number of trapped atoms because of modulation is too fast to allow the system to collect cold atoms in the trap; in other words the time during which light is present in the cell is too small compared to the characteristic time of forming of the trap.

Frequency modulation of repump laser: this technique has the advantage to enlarge the frequency spectrum of the repumping laser and hence to compensate an accidental drift or shift in the repumping frequency during a frequency scan of the main laser. Anyway the power per frequency unit is reduced proportionally to the modulation amplitude; this gives a reduction in the number of trapped atoms. First of all, we have measured the trap signal width as a function of the repumping laser frequency, i.e., as a function of the modulation amplitude voltage applied

New detection system for TRAPRAD

39

to the modulation input of the current stabilisation system of the diode laser. It resulted an amplitude of 1 mV for the full trap width at half maximum. We then expect that the power per unit of frequency goes as P/Vmod , for peak to peak modulation amplitudes Vmod > 1 mV. This fact is shown in g.(2.2): in the rst part of the graph we clearly see a straight line, which con rms the following fact: the main e ect of the modulation on the Rb trap is to reduce the repumping power per unit of frequency. The last part of the graph shows a saturation, as expected from two-level system theory.

Trap Signal (a.u.)

25

No modulation Modulation

20 15 10 5 0

2

4

6

8

10

P/Vmod (mW/mV) Figure 2.2: trap signal as a function of the power per unit of frequency of the repumping laser.

During my work we have developed a new detection and acquisition system, based on a very sensitive CCD camera from Hamamatsu (model ORCA) which allows us to acquire an optical image of the cold cloud; the principles of operation of this system are described below.

40

2.2 Choice of the signal The leading idea is to understand from a frame of the cold cloud, how many atoms are trapped; this is very important to evaluate a priori the signal to noise ratio obtainable in any kind of experiment with cold Fr atoms. For this purpose the rst very important step is to de ne a signi cant quantity S as the signal, ideally proportional to the number of atoms. One logical choice is to sum the digitised signals from each pixel of the frame, avoiding to consider the pixels which in any case only contribute to the noise; then we de ne a so called Region Of Interest (ROI) around the trap image. In order to give a de nition for the ROI, we can take a look at the pro le of the trap along two axes x and y (horizontal and vertical with respect to the CCD device). The idea is to Figure 2.3: Spot from a He-Ne laser, incident on a black screen. t the pro les with gaussian funcThe light power entering the detection system was about 9 pW. The tions (exp( 2  ( xwxxc )2 ), where xc exposure time was 1 s. is the coordinate of the center of the spot and wx the width of the gaussian and similar for y) and take as region of interest an ellipse with (xc ; yc ) as center and 2wx;y as diameters for the x and y axes respectively. As an example we can see in g.(2.3), the acquired image of the spot generated on a black screen from a He-Ne laser beam, used to simulate the image of a MOT cloud (elliptical shape) with a possible choice of the relative ROI. Now that we have chosen the ROI, we can give the de nition of the raw signal Sraw : Sraw =

X

pixels(i)2ROI

S (i):

This is not our nal signal quantity, because we did not account for the presence of a

New detection system for TRAPRAD

41

background signal. We have to subtract this o set in order to obtain the true signal S : S = Sraw

Sbackground ;

with Sbackground the raw signal coming from the detection system when no trap is present.

2.3 Calibration of the signal S We must now calibrate the signal S with respect to the number of atoms in the MOT cloud. This can be performed in two steps: rst the calibration of the CCD in terms of the light power entering the zoom lens. Then the calculation of how much light is emitted from the single atom and reaching the zoom lens (i.e. calculations of uorescence rate and solid angle).

2.3.1 Calibration S $ power We choose to calibrate the CCD with a spot obtained from a laser beam incident on a black screen. We used three di erent wavelengths: 633 nm from a He-Ne laser and from the trapping Ti:Sa laser 718 nm and 780 nm; the last two are respectively the wavelengths for trapping Fr and Rb atoms. The black screen is tilted with respect to the laser beam, in order to obtain an elliptical shape for the spot, as similar as possible to the one obtained from the MOT. The power coming from the spot has to be low (< 1 nW), because this is the order of magnitude we could expect from a simple calculation of the power entering the detection system from the MOT uorescence; if we consider that the atom is approximately saturated on the D2 transition, the result is straightforward: P sat (Rb) =

hRb hc=(780 nm) = = 4:8 pW 2Rb 2  26:5 ns

hFr hc=(718 nm) = 6:6 pW = 2Fr 2  21 ns Taking into account the solid angle of the order of 10 3 covered by the CCD detection system P sat (Fr) =

and a number of trapped atoms of  104 we have an estimate of the maximum detectable power of a few tenths of pW. This is the reason why we use a black screen. The beam is also attenuated by a variable lter and one or two neutral lters (actually when we changed wavelength, we paid attention to measure again the transmittance of the lters, because it was found to change according to the wavelength). The power re ected from the screen is measured

42 with a commercial power meter when no lters are present and then corrected thanks to the lters calibration. Frames were taken for di erent powers, at the three wavelengths 633 nm, 718 nm, 780 nm. We took frames for 1 s exposure time, and also 100 ms @ 633 nm in order to check that signals were 10 times less. We see from the graphics in g. (2.4) that the behaviour of the detector is linear. The signals are also linear with respect to the exposure time: the calibration for 1 s is 546:2=54:54 = 10:01 times the calibration for 100 ms, @ 633 nm (see table (2.1)).

Figure 2.4: Calibration S $ power entering the camera lens, for the three wavelengths 633 nm (He-Ne), 718 nm (Fr) and 780 nm (Rb).

(S=1000) = P (pW) He-Ne, 100 ms He-Ne, 1 s Fr, 1 s Rb, 1 s

54.54 546.2 461.2 345.6

Table 2.1: Calibration S $ power entering the camera lens, obtained from the ts of the data reported in g. (2.4).

2.3.2 Power emitted by one atom The problem is now to deduce how many atoms are present in the MOT cloud, from the light power obtained from the analysis of the frame. We then have to know how much power is emit-

New detection system for TRAPRAD

43

ted by the single atom. We can treat the problem of the interaction of the Fr atoms with laser light in the MOT region with the well known Bloch formalism. We provide here a simpli ed scheme of this problem, in which we consider a six level atomic system with two di erent laser eld interacting (main and repumping laser). In this way we could take into account population and induced coherences with atomic levels non involved in the cycling transition 72 S 12 ;F = 132 ! 72 P 32 ;F = 152 used for trapping and give a precise estimation of the upper level population to calculate the intensity of the uorescence emitted by a single atom. First of all, let us de ne the atomic system. For simplicity we consider only the levels involved in trapping transition and optical pumping in the ground hyper ne state of 7S level. A picture of the system considered is shown in g.(2.5). Optical pumping in such a scheme is caused by the decay from the upper level Figure 2.5: scheme of the levels of Fr involved in trapping transitions; 2 7 P 32 ;F = 132 to the 72 S 12 ;F = 112 : the dashed arrow indicates possible radiative decays; solid arrow indicates level 72 P 23 ;F = 132 is in fact populaser induced transitions; frequency separations are taken from [56]. lated from the non-resonant main laser eld (detuning is a few tens in natural linewidth units). For further simpli cation we neglect the far o resonant eld connecting b with c and d levels: repump laser is tuned near the a ! c transition so the detuning from the b ! c and b ! d transitions is of the order of the Fr ground state hyper ne splitting (47 GHz); the inclusion of

44 such a term in the Hamiltonian matrix can be useful to calculate the AC Stark shift of the levels, which is out of the goal of this dissertation. An important approximation is to consider as degenerated all the Zeeman sublevels: this is justi ed by the fact that, assuming a trap size of 1mm and a magnetic eld gradient of 10G/cm, the maximum rst order Zeeman shift is of the order of 1.4MHz versus a linewidth of the main transition of 7.6MHz. The Hamiltonian in the Electric Dipole approximation can thus be written as a 6  6 matrix: 0

H=~

B B B B B B B B B B B B @

0 0 A 0 !b 0 A 0 !c A 0 0 0 C 0 0 C 0

A

0 0 !d 0 0

0 0 C C 0 0 0 0 !e 0 0 !f

1 C C C C C C C C C C C C A

(2.1)

where we denote the levels with a; b; c; d; e; f and we set !a = 0; A; C are the Rabi frequencies A = 12 (A0 ei!r t + A0 e i!r t ) and C = 12 (C0 ei!p t + C0 e i!p t ), in which !r and !p are the proper laser eld angular frequencies, i.e. main for C and repump frequency for A. Dipole connection between e and f with c and d is zero because of parity symmetry reasons; in the same way there is no decay (and then collection of population) to c and d from e and f states. The evolution of the density matrix  is given by _ =

1

i

~ [H; ] 2 f

; g

(2.2)

where we introduce the relaxation matrix 0

0 B B B 0 B B B 0 =B B B 0 B B B 0 @ 0 Obviously we have c = d and e = f .

0 0 0 0 0 0

0 0

c 0 0 0

0 0 0

c 0 0

0 0 0 0 0 0 0 0

f 0 0 f

1 C C C C C C C C C C C C A

New detection system for TRAPRAD

45

Equation (2.2) gives correct results for the evolution of coherences with the right relaxation coecients, but the collection of population by radiative decay from upper levels has to be added by hand, taking into account the hyper ne structure; for this purpose we have used the 6j coecients: the A ! B transitions have been weighted with 8 < :

1 FB FA I JA JB

92 = ;

(2FB + 1)(2JA + 1)

Since  is hermitian we have only to consider the evolution of the diagonal and upper triangle elements; we obtain 8 11 _a = 2Im[(ca + da )A] + c ( c + d ) + f e (2.3) 13 39 5 28 _b = 2Im[(eb + fb )C ] + c ( c + d ) + f e + f f (2.4) 13 39 _c = 2Im( ca A) c c (2.5) _d = 2Im( da A) c d

(2.6)

_e = 2Im( eb C ) f e

(2.7)

_f = 2Im( fb C ) f f = (_a + _b + _c + _d + _e ) 1

 ac _ = i[(c a )A dc A ac !c ] 2 c ac 1

 da _ = i[(a d )A dc A da !d ] 2 c da 1 _be = i[be (!b !e ) + (e b )C + fe C ]

 2 f be 1 fb _ = i[bf (!f !b ) + (f b )C + ef C ]

 2 f bf _dc = i[ac A da A + (!d !c )dc ] c dc fe _ =

i[ eb C + bf C  + ef (!e

!f )] f ef

(2.8) (2.9) (2.10) (2.11) (2.12) (2.13) (2.14)

Equation (2.8) is valid since the system is though as closed, i.e. no population is \lost" in other non considered levels. In order to simplify equations we introduce new slowly varying quantities r de ned as ryx = yx ei!L t and, to conserve the hermitian condition, ryx = rxy  ; this new variables take into account the \rotation" given from external elds to coupled coherences, i.e. the ones corresponding to the terms of hamiltonian di erent from zero. Then, by substituting, in equations from (2.9) to (2.12), and by neglecting all the terms oscillating at 2!p ; 2!r ; !p ; !r (Rotating Wave Approximation, RWA) we obtain

46

rac _ = i(c rda _ = i(a rbe _ = i(e rfb _ = i(b





A A 1 a ) 0 + idc 0 + i(!c !r )

r 2 2 2 c ac   A A 1 d ) 0 idc 0 + i(!d !r ) + c rda 2 2 2   C0 C0 1 C b ) + ife + i(!e !b !p )

c rbe + ife 0 2 2 2 2     1 C C f ) 0 + i(!f !b !p ) + f rfb ife 0 2 2 2

The other two non vanishing coherences are dc and fe , with evolution equations A A _dc = irac 0 irda 0 i(!d !c )dc c dc 2 2 C0 C0 irfb i(!f !e )fe f fe fe _ = irbe 2 2

(2.15) (2.16) (2.17) (2.18)

(2.19) (2.20)

Once we set ddt  0 this six equations constitute two independent systems of three equations in three variables, considering the populations as known terms. In the equations for the other coherences we neglect all the terms oscillating at the fundamental frequencies !r and !p ; this implies that, after a transient, all the coherences involved go to zero following an exponential decay law, modulated by a sinusoidal oscillation at a frequency given by the di erence of energy of the involved states (i.e. the steady state solution for this coherences is zero); this is not so useful for our goal but is an expected result, because any term of the hamiltonian induces these coherences. Finally let us write the equations for the diagonal terms of , which are only coupled with the non vanishing coherences, in the RWA 8 11 _a = Im[(rca + rda )A0 ] + c ( c + d ) + f e 13 39 5 28 _b = Im[(reb + rfb )C0 ] + c ( c + d ) + f e + f f 13 39 _c = Im(rca A0 ) c c _d = Im(rda A0 ) f e _e = Im(reb C0 ) f e _f = Im(rfb C0 ) f f

To solve this system we use numerical solutions for the stationary coherences obtained from the two independent systems above. This is not an independent set of equations (it's easy to

New detection system for TRAPRAD

47

see that the sum of right sides of equations gives zero), because of the condition X

i

i = 1

(2.21)

has to be satis ed at any time (closed system hypothesis). If we are mainly interested in the determination of the populaParameter name Value tions e , f , d and c of the atomic system in a stable MOT, !d !r 0 we can search a stationary solution of the system; this can ob!c !r 1072 c viously be achieved by imposing the condition that all the time !f !b !p 5 f derivatives are zero: the system of equations becomes algebraic. !e !b !p 77 f In this way, we can solve the three variables systems given from C0 1:56 f equations (2.17), (2.18) and (2.20), and from equations (2.15), A0 0:218 c (2.16) and (2.19), considering the populations as known terms; Table 2.2: settings of the param- then we substitute the obtained solution in the equations for eters for numerical solution. the populations, and nally we x parameters for a numerical solution (see table (2.2)). The values of C0 and A0 can be obtained from intensity measurements of the six MOT beams considered as uniform, and from the saturation intensity for D2 and D1 line of Fr found in literature [22]. Finally in [17] we found the values c = 34:0MHz and f = 47:5MHz, allowing us to express all the relevant parameters listed in table (2.2) in terms of the natural linewidth of the 7P levels of francium. We put !f !b !p = 5 f only as an example, because this is a reasonable condition reported in [57], in order to obtain a stable trap.

2.3.3 Checking the system: the rubidium MOT Our trapping laser is a Ti:Sa ring laser. This allows us to tune its frequency also on the D2 Rb line at 780nm, and trap a cold sample of Rb atoms. This is a good check for the conditions of the whole system (vacuum in the cell, coating and neutraliser eciency, shape and position of the trap, polarisation and intensity of laser beams,...) when Fr atoms are not available. For this purpose, we also use a diode laser at 780nm to achieve repumping in a di erent scheme with respect to Fr MOT: this is made by tuning the repumping laser on the 52 S 12 ;F =2 ! 52 P 32 ;F =3

48 transition; this correspond to the levels a and e of the Fr scheme reported in g.(2.5) which is similar for Rb as for all alkali atoms. If we want to use Rb MOT to test also the detection system, we have to solve Bloch equations for Rb too. In the case of Rb the system of equations is much simpler because of the use of the D2 line also for repumping: in this way, c and d levels can be considered very far o resonant and thus not involved in the light scattering processes, i.e. c = d = 0 at any time: in this case we can consider a four level atomic system instead of a six level system as for Fr, as shown in g(2.6). The method to solve this system is anyway the same used before and we don't report it here. In table (2.3) we report the results for the ping transitions; dashed arrow indicates possible radia- conversion power $ number of atoms for both tive decays; solid arrow indicates laser induced transi- Fr and Rb, and for three di erent values of the tions. detuning of the main laser with respect to the resonance center; red detuning is necessary to cool down the atomic sample, but its optimal value depends on many parmeters (intensity and diameter of MOT beams as an example) and we can not measure it for Fr; the values 5 f and 2 f are reasonable limits [57]. In the last row of table we report the number of atoms corresponding to a detected power Pdet = 1 pW, taking into account the small solid angle of 1,510 3 covered by the detection system. Figure 2.6: scheme of the levels of Rb involved in trap-

2.4 Noise analysis We can distinguish between two kinds of noise: the noise intrinsic to the CCD, measured when no light enters the detection system (in practice camera with the diaphragm completely closed) and the noise coming from the background light (essentially the light from the Ti:Sa laser). The simplest way to measure the noise is to take a series of frames, evaluate the signal S for

New detection system for TRAPRAD

49 210 Fr

Atom

85 Rb

Detuning

5 f

2 f

0

5 f

2 f

0

f

0,031

0,16

0,47

0,031

0,16

0,49

P=atom (pW)

0,47

2,1

6,2

0,34

1,6

4,7

1400

300

110

1900

400

140

Pdet = 1 pW) Ntrap

Table 2.3: Relevant quantities for the conversion Power $ Number of atoms; P=atom is the power emitted by the single atom in the entire solid angle, while Pdet is the power entering the zoom lens and detected by the CCD.

each frame and calculate the variance of this quantity for the acquired series. By this way we can measure the intrinsic noise (with closed diaphragm) and the background noise (with open diaphragm and no trap). The noise was measured several times: we found that the background noise is always much larger than the intrinsic noise. Since the considered quantity S is the same we use for the evaluation of the trap signal, thanks to our calibrations we can directly express the noise in terms of power (pW) and number of trapped atoms.

2.4.1 Weighted subtraction of the background In order to improve the quality of the frames, we can subtract from each acquired image a reference background image. In practice, the background image is obtained as an example from the average of a series of 5 or more frames taken without trap. The resulting images are more uniform, and then a weak trap is more easily detected by eye. Note that the noise (the variance of S ) does not change, since we only subtract an o set. Usually a large part of the background noise is due to power uctuations of the main laser: in a simpli ed model, we can say that the background light is directly proportional to the main laser power. It is possible to compensate in part these uctuations. We de ne a second ROI, named background ROI, spatially shifted with respect to the trap ROI and with the same shape and dimension for simplicity. Since this ROI is placed in a region where no trapped atoms are present, it directly monitors the background light. Let us call S bg and S trap the signals from the background ROI and the trap ROI. S (acq) refers to the acquired raw frames (usually taken to try to see the trap), whereas S (ref) refers to the reference background image. With the simple subtraction, the considered image is obtained from the formula: (acq - ref), giving for the signal the formula S trap (acq) S trap (ref). In order

50

Figure 2.7: logical scheme of the trap images acquisition program; N is the number of images averaged to obtain the background image, M is the total number of trap images acquired,  is the exposure time for every image.

to correct for background uctuations, we now consider the weighted subtraction acq

S bg (acq)  ref S bg (ref)

which gives the following elaborated signal: S w  S trap (acq)

S bg (acq) bg  S (ref) S bg (ref)

Note that electronic o set from raw CCD signals have to be taken into account: instead of the raw frames acqraw and refraw we have to use acq = acqraw

o set

New detection system for TRAPRAD ref = refraw

51 o set

An acquisition program developed using the LABVIEWTM platform allows us to perform this analysis automatically and in real time; the logical scheme of this program is shown in g.(2.7). Acquired images are 32-bit signed raw images. Unfortunately, with this scheme, we are not able to acquire more than four frame per second without a non negligible dead time between two consecutive images; for this reason, we developed also a version of the program which initially acquires a given number of images at a given acquisition time of the CCD camera, and then perform the analysis with the same scheme described above; the maximum rate we could achieve with this technique is about 50 Hz. Particular care has to be taken in the alignment of the six

Figure 2.8: on the left, raw image without weighted background subtraction; on the right the same image, when improved, shows a Rb trap of about 80 atoms; noise was measured to be less than 20 atoms.

MOT beans because we found the background very sensitive also to a small misalignment; light scattered from the edges of the cell windows as an example gives an important contribution to the noise. Alignment of the CCD camera is made in such a way that behind the cold cloud we can individuate a dark region (clearly visible on the left image of g.(2.8)) due to a Rb reservoir sealed to the cell; this further reduces uctuations inside the trap ROI and makes trap more visible to the naked eye on the display of the acquisition PC. Background ROI is chosen in a region where scattered light is clearly visible, in order to well measure and then compensate

52

Figure 2.9: number of trapped Rb atoms as a function of Ti:Sa frequency; noise level is less than 20 atoms.

intensity uctuations. Thanks to this procedure we are able to detect a rubidium MOT with a small number of atoms (even less than 100); this is very important when we work with radioactive francium atom, because of the small ux of Fr ions and so the small density of Fr atoms in the MOT cell, can lead to a maximum number of trapped atoms of a few hundreds at the beginning of a set of measurement during a beam time, before a proper optimisation of all trap parameters. In g.(2.8) we show on the left a raw image of the trap region, where no trap is visible by eye, whereas on the right, the same image, after the weighted subtraction, shows at its center a cold cloud of about 80 Rb atoms (in the hypothesis of 5 f detuning). The number of trapped atoms could then be plotted as a function of the Ti:Sa frequency. In g.(2.9) an example of such a signal is reported; when the laser is o resonance a noise level less than 20 atoms is clearly visible.

New detection system for TRAPRAD

53

2.5 First tests with the Rb MOT

















































Figure 2.10: 3D image of the trap in false colours; signal is expressed in digital units; image refers to 600 trapped atoms ; spatial coordinates are measured in pixels of the CCD sensor.

The new acquisition system described above allowed us to perform tests on the apparatus, using the Rb MOT, during about one year between two beam times at the Legnaro facility, in order to determine the optimal values of some of the trap parameters. A typical 3D image of the Rb MOT is shown in g.(2.10). These measurements, described here, have been fundamental to obtain the results with the Fr MOT described in the next chapter.

54

2.5.1 Number of atoms as a function of the laser power We measured the trap signals for di erent laser intensities. The results are presented in g.(2.11) as a function of the average intensity of all the six laser beams in the MOT cell. The assumption that we saturate the D2 transition ( rst graph) can be pessimistic for the resulting number of atoms, whereas the assumption that we are 5 f below the transition is probably optimistic. These results can be considered as lower and upper limits for the number of trapped Rb atoms. Furthermore the noise due to light scattered from the cell and environment increases linearly with the laser power; so, if the number of atoms, after a certain intensity, saturates or even begins to decrease, at higher intensities the signal to noise ratio tends to zero. These conFigure 2.11: (a) number of trapped Rb atoms vs. laser intensity in the siderations demonstrate that it hypothesis of saturated transition; (b) number of trapped Rb atoms vs. is not convenient to use maxlaser intensity in the hypothesis of -5 f detuning. imum power, while measure-

New detection system for TRAPRAD

55

MOT FWHM (pixels)

7 6,5 6 5,5 5 4,5 4 1

2

1,5

2,5

3

Anti-Helmholtz coils current (A) Figure 2.12: FWHM Rb atoms as a function of current in the anti-Helmholtz coils. ments give an indication of the best work conditions. Once we choose the intensity for Rb trap, the value for Fr has to take into account the di erent saturation parameter IFoptr =

IFsatr opt sat IRb IRb

opt ' 1; 8 IRb

where I sat represent the saturation intensity for the cycling transition useful to magneto optical trapping of the alkali atom considered.

2.5.2 Reproducibility of the trap position An essential requirement for our detection system (and a reasonable requirement for the experiment itself...) is the reproducibility of the position of the MOT: if the atomic cloud goes away from the ROI we lose the signal computed by the acquisition program. In principle the cloud can be slightly shifted from the null magnetic eld region because of the radiation pressure forces

3

Number of trapped atoms (10 )

56

7 6 5 4 3 2 1 0

1

1,5

2

2,5

3

Anti-Helmholtz coils current (A) Figure 2.13: number of trapped Rb atoms as a function of current in the anti-Helmholtz coils. are not well balanced in the three directions or due to a defective setting of the laser beams polarisations; this e ect could be very undesirable when we switch from tests on Rb MOT to measurements on Fr MOT during beam time. We checked indeed that the cloud slightly moves when we change some parameters (the alignment of the six trapping beams, the total power of the trapping laser from 200 to 600 mW), but it stays inside the ROI. Therefore, each time, the Fr trap position should reasonably match the Rb trap one.

2.5.3 Changing the magnetic eld gradient An atom entering the region around the zero of the magnetic eld produced by the two antiHelmholtz coils is subjected to a spring force approximately proportional to the magnetic eld gradient, for short distances from the center of the cell; this force is responsible for the localisation

New detection system for TRAPRAD

57

of the cold cloud in a small region around the position of equilibrium. Thanks to the CCD camera we are able to measure the size of the trap as a function of the magnetic eld gradient which is proportional to the current in the anti-Helmholtz coils. In g.(2.12) results are shown in terms of FWHM of the trap measured in pixels; this is obtained by tting the pro le of the trap along the x axis of g.(2.10) with a gaussian function. At current greater than 2 A we observe a better localisation of the cloud. In spite of this result we also observe a reduction of the number of trapped atoms for the same values of the current (see g.(2.13)) and at current lower than 1 A too. After these measurements we set the current at 1,5 A for Rb trap and we use the same magnetic eld for Fr trap, as the Lande factors for the two atoms are of the same sign and order of magnitude.

Chapter 3

First results with the Fr MOT You can't ask me all the questions and I can't give you all the answers. Jose Saramago in \The Gospels according to Jesus Christ" (1991)

After about one year of tests 210 on the whole apparatus, espeFr 209 Fr cially on the new possibilities offered by the new acquisition sys0.5 tem, we had, on July 2007, two days of beam time at the accelerator, in which we acquired the rst images (and data too) on 0 1000 500 1500 the 210 Fr MOT. Some image imTime (s) Figure 3.1: radioactive decay rate of 209 Fr and 210 Fr measured at the proved with ImageJ software [58] last Si detector 1 m apart from the MOT cell, during optimisation of is reported in g.(3.2). 3

Decay Rate (10 dec./s)

1

the electrostatic optics of the transport line; the signal relative to 209 Fr, faster sensitive to changes, is useful to achieve the optimal alignment.

We were also able to trap and image a 209 Fr sample, even if the

First results with the Fr MOT

59

max

min

Figure 3.2: ve images of the 210 Fr MOT elaborated to enhance contrast: from left top 220 atoms, 450 atoms, 560 atoms, 930 atoms and 1100 atoms; last image is a 3D representation of the higher signal of 8000 trapped atoms; column on the left shows the lookup table.

Residuals of Smoothing

Number of Trapped Atoms

60

60

40

20

0

-20 120 20

140

160

180

200

20

40

60

80

0 -20

Frequency (MHz) Figure 3.3: frequency scan of the trap laser (smoothed signal); residuals of smoothing have a RMS equal to the acquisition noise level (red lines).

energy of the primary oxygen beam was not optimised for this isotope. In g.(3.1) a simultaneous registration of the 209 and 210 isotopes decay rate is shown. The signal is taken by a SSBD detector with an angular acceptance of 2,210 3 srad and is able to discriminate the two isotopes from the energy of emitted particles. The 209 Fr is used here for optimisation of transport, due to the shorter lifetime (72 s versus 275 s of 210 Fr), hence changes in secondary beam line alignment have faster consequences on the signal from this isotope.

3.1 Trap signal In g.(3.3) the very rst Ti:Sa laser scan over the trap frequency of the July beam time is shown. The very good conditions of detection allowed us to achieve a noise level of about 10 atoms, and hence to reveal a cold cloud of a few tens of Fr atoms. Thanks to the decay rate measurement

First results with the Fr MOT

61

Number of trapped atoms

150

100

50

0

100

200

300

400

Time (s) Figure 3.4: Fr trap signal (black curve) and correspondent simulation (red curve); at t'2 s ionic beam is sent on the neutraliser; radioactive decay is taken into account during di usion in the simulation.

we can estimate an ionic current of 4105 ions/s. Frequencies of main and repumping lasers measured with our commercial wavemeter at the maximum of the trap signal are reported in table (3.1) and are consistent with the one reported in [59]; error of 30 MHz is due to the instrumental resolution of the wavemeter. In g.(3.4) is shown that the simulation of the experiment with di usion model and rate equations for trap population, still remains adequate for Fr trapping process. Radioactive nuclear decay must be taken into account during di usive migration of Fr ions towards the surface of yttrium foil as in the trap population.

62

Number of trapped atoms

500

400

300

200

100 magnetic field on 0 10

20

30

40

50

Time (s) Figure 3.5: Fr trap signal; at t'10 s magnetic eld is turned on, while ionic beam continuously hit the neutraliser; a number of 350 Fr atoms is trapped in the steady state condition.

Anyway, following equations (1.3), since r and L are much smaller than W and C as expected in our 210 Fr 417412,50(3) 366898,75(3) case, the di erence in the number of trapped atoms 210 Fr 417415,15(3) 366897,48(3) with respect to the case r = 0 is of a few percents, Table 3.1: optimal laser frequencies for trap- and hence negligible if compared also with our low ping of 210 Fr and 209 Fr; errors in parenthesis cordetection noise for a trap of a few hundreds of atoms respond to the wavemeter resolution. as in g.(3.4). Isotope

main (GHz)

repump (GHz)

In this situation of continuous loading of the trap, we obtained at the beginning a maximum number of trapped atoms around 100; we suddenly tried to improve this result, rst of all by increasing the francium production. In a condition where primary oxygen beam was set to the maximum allowed current (limited only for radiation safety reasons), we measured a record rate

First results with the Fr MOT

63

of 210 Fr at the last SSBD of 3 kHz, and a trap population in continuous regime of 350 atoms, as shown in g.(3.5). Another good solution to load the Fr trap and trap even more atoms could be the accumulation of ions for a few lifetimes in the neutraliser at room temperature, where di usion is very slow, and the sudden release of Fr in atomic form by rapid heating of the yttrium; the measurements performed with this technique, taking advantage also of the very high production rate, are reported in sect.(3.3).

3.2 Trap also with cold neutraliser While waiting the time necessary for accumulation, we observed a completely unexpected phenomenon. Images of even 80 trapped atoms (see g.(3.6)) were observed even with the cold neutraliser. The signal was not spurious as con rmed to us by the fact that it disappears when the magnetic eld was turned o . Unfortunately, image quality is depleted, due to the acquisition of background image when the neutraliser was hot. In fact, at 1000 K, yttrium is incandescent and emitted light contributes in a not negligible way to the stray light in the cell. We want to remark now that this kind of signal was only observed with the higher Fr production rate. A possible explanation could be found in the direct and instantaneous neutralisation of Fr ions directly at the surface of the catcher. Anyway at this beam energy, for a massive ion as Fr with respect to Y, the probability of back scattering is very low [49] and no ions are implanted near the surface, i.e. the implantation distribution is very concentrated around the mean implantation depth d, as shown by TRIM simulation. Another e ect to take into account, which can be well considered to explain the observed behaviour, is sputtering; in the many body collisions dynamics of this e ect, it is possible that incoming ions kick back the previously implanted ions, even from a distance comparable with d and with characteristic times faster than those of di usion. Moreover, for a massive and intense bombarding beam as in our case, also local melting of the bulk material was observed in previous experiments [60], leading to an enhanced sputtering yield. This last observation is also consistent with the fact that we observe the phenomenon only with high ionic beam intensity and we never observe it with the Rb ionic beam, in which ions has a mass comparable with that

64

Figure 3.6: on the left, image with enhanced contrast, of a trap of 80 atoms observed with the cold neutraliser; on the right, surface plot of the image.

of Y. It would be interesting to study if, for example, we can observe a threshold in intensity of the incoming beam.

3.3 Di usion time of Fr in yttrium catcher The optimal operating temperature for the neutraliser foil is estimated to be, from measurement performed on Rb and described in sect.(1.4.1), around 1000 K; in these conditions the di usion time is of the order of a few tens of seconds, short enough with respect to the lifetime of 210 Fr to be not a ected from losses of Fr atoms via nuclear decay inside the yttrium. From the Arrhenius' law it is straightforward to estimate that at room temperature (300 K), the di usion coecient could be 20 orders of magnitude lower with respect to 1000 K: if ions are implanted at a certain distance from the surface we can consider that they remain there until temperature is increased; if this is made by suddenly raising the heating current to the operating value, we are in the situation described by equation (1.8), in concerning the neutral current released from neutraliser. The total number of implanted ions can be estimated considering that equilibrium between incoming current I0 and radioactive decay r Nimpl gives rise to a time dependence of

Number of trapped atoms

First results with the Fr MOT

65

400

Experimental data Fit curve

300 200 100 0 100

50

150

Characteristic release time (s)

Time (s) Experimental data Fit curve

50 40 30 20 10 0

960

980

1000

1020

Temperature (K) Figure 3.7: upper graph: experimental data and curve t with a curve given by equation (1.8) with

= 0:00363285 s lower graph: di usion time as function of temperature and t curve using an Arrhenius' law; data and error bars are given from ts at di erent temperatures. 1;

r

66 the form Nimpl (t) =

I0 r

1 e

rt



(3.1)

We measure the trap signal obtained after 600 s (which correspond to 2,2 radioactive lifetimes) of accumulation for ve di erent temperatures of the neutraliser; at the higher temperature of 1033 K we obtain the absolute maximum number of trapped atoms of more than 8000; a typical signal is reported in the rst plot on g.(3.7). In these measurements we also observe an e ect due to the radioactive decay, because of data are signi cantly better tted if the factor exp ( r t) is considered in the model. In the second graph of g.(3.7) the results for the tted parameter d are reported as a function of temperature (error bars are given from t). As for Rb, we used the TRIM code [52] to evaluate the mean implantation depth for Fr in Y, which gives a value of 51  A; release time data are then tted according to the Arrhenius' law and t results are: 1000 = (16; 5  1; 4) s

Ea =kB = (22000  3000) K

where 1000 end Ea should have, at this point, a clear de nition. The measured di usion coecient at 1000 k is then D1000 = (3; 9  0; 3)  10

15

cm2 s

1

This is to our knowledge the rst measurement of di usion parameters of francium ions in yttrium and the rst time that di usion time is determined from the study of the time evolution of the signal from a magneto optical trap.

3.3.1 Release fraction According to [50] it is possible to de ne a parameter which measure the loss of atoms due to nuclear decay during the di usion towards surface; this is the so called \release fraction" which gives the percentage of radioactive ions neutralised before the decay and then suitable for p trapping; in other words we could think to the release fraction "( r ) = exp ( 2 r d ) as a sort of neutralisation eciency. From di usion time measurement we determine the release fraction as a function of temperature as shown in g.(3.8). In the same gure we report also the predicted release fraction for the isotope 209 Fr that we are able to produce and trap; as already discussed, the apparatus was not optimised for

First results with the Fr MOT

67

1

Release fraction

0,8

0,6

0,4

0,2

210 209

0

960

980

1000

Fr (measured) Fr (predicted)

1020

1040

Temperature (K) Figure 3.8: release fraction measured for isotope 210 from the di usion time as a function of temperature and expected for shorter lived 209 isotope.

the production of this isotope, so we didn't perform systematic measurements on 209 Fr, but we can expect that, supposing the same di usion coecient as for 210 Fr, due to shorter lifetime, we would have to construct a neutraliser with higher operating temperature to obtain a release fraction signi cantly higher than 50%.

3.3.2 Estimation of trapping eciency From the t results of the acquired curves at di erent temperatures it is also possible to estimate the trapping eciency of the francium MOT. In fact, the free parameters of t are the release time and an amplitude factor proportional to the total number of ions implanted in the catcher bulk during accumulation in cold yttrium; more in detail this amplitude factor A must be equal

Number of trapped atoms

68

150

Experimental data Fit curve

100

50

0 300

320

340

Time (s) Figure 3.9: experimental data and t curve for accumulation and subsequent release and trapping of 209 Fr. 0; 9I L to p 0 , where I0 is the incoming current of 4  105 ions/s, determined from decay rate r 4CW measurement and transport eciency; the correction factor 0,9 takes into account, according to eq.(3.1), the fact that 600 s are not enough to reach the steady state of number of implanted I ions 0 ; furthermore, from rising time measurement of the trap signal, we estimate a value of r 1=C ' 1; 6s. Finally the value we obtain for the ratio L=W is 2,310 4 which gives an eciency 210 =

L=W 1 + L=W

' 2; 3  10

4

We repeated the same measurement also for the other isotope 209 Fr and we obtain also in this case a good t of the experimental data (see g.(3.9)); estimated eciency is then 209 =

L=W 1 + L=W

' 3; 2  10

4

First results with the Fr MOT

69

in agreement with the other isotope as expected. This result for the trapping eciencies  is not surprisingly low, because is of the same order of magnitude we could estimate from calculation of rate coecients L and W performed in chap. 1. Previous works [46] obtained a record trapping eciency of 0,56 with the \long" lived (t1=2 ' 4; 9 min) but in a completely di erent experimental setup, that is with a closed cell (i.e. not connected to pump during trapping), in which it is possible to achieve very small value of W. In next chapter we will be discussed a possible development to improve such a low eciency, by the use of LIAD e ect from OTS dry- lm coating of the cell, which was for the rst time observed during this work.

Chapter 4

LIAD e ect from dry- lm coating Whatever you do will be insigni cant, but it is very important that you do it. Mohandas Karamchand Gandhi

In a wide class of spectroscopic experiments, coating of a common glass cell is a typical arrangement to avoid strong interaction of atoms with the cell walls, generating sticking or spin relaxation. Light-induced desorption from organic lms upon weak illumination has been observed in the 90s with Na and Rb in PolyDiMethylSiloxane (PDMS) coated cells. Main features are the weak adsorption energy of lm, the di usion of atoms inside the lm itself and the high desorption eciency. The e ect, named LIAD [61], has been observed so far with Na, K [62, 63], Rb [61] and Cs [64] in cells coated with PDMS, OctamethylCycloTetrasiloxane (OCT) and paran [65, 66]. Rb atoms desorbed from a PDMS lm have been used to load a MOT, and very fast and ecient loading has been observed [34]. The possibility of build up atomic sources controlled only by light, was in the last years one of the main reason in studying the features of LIAD e ect from organic coatings. A class of such compounds named dry- lm, widely used for its good behaviour in high vacuum conditions [67], up to now never showed this e ect; in this chapter we report the rst experimental evidence of non-thermal light induced atomic desorption from OctadecylTrichloroSilane (OTS) dry- lm. This is very interesting in applying LIAD e ect

LIAD e ect from dry- lm coating

71

t2

δ LIAD(t)

2

tmax

1

t1 0 100

200

300

400

500

Time (s) Figure 4.1: typical LIAD signal; at t=t1 desorbing light is switched on, LIAD reaches its maximum at t=tmax and at t=t2 desorbing light is switched o ; uncertainty for each point is evaluated using the root mean square of points at t
to the loading of a magneto-optical trap; in particular OTS is used in MOT experiments with short lived radioactive atoms [68]. We will see that desorption eciency is slightly better with respect to PDMS with a lower limit pressure achievable: this could give an improving in the trapping eciency.

4.1 LIAD description and signal When a coated cell is shined with light, an increase in the vapour density is observed, the density reaches a maximum and then starts decreasing towards the value of thermal equilibrium n0 as shown in g.(4.1). Two parameters characterising LIAD e ect are the maximum light-induced max and the rate of the atoms relative variation of the atomic density n in the vapour phase LIAD desorption at the time when the desorbing light is switched on R; this two parameters are de ned

72 as following: max = LIAD

nmax n0 n0

(4.1)



1 dn R= n0 dt t!t

(4.2) 1

While the rst depends also on the particular construction of the cell, because of its absolute value depends also on the characteristic time of di usion through the capillary of the alkali reservoir, the second could be used to de ne a new parameter characterising the desorption eciency, while its value is taken at the beginning of the process.

4.2 One dimensional di usion model This behaviour was interpreted using a di usion model [69] that showed that a simple interaction of light with atoms at the surface of the coating is not enough to explain the density variation induced by light: also di usion of atoms in the bulk of coating has to be taken into account. At a given temperature T and without desorbing light, such a process can be characterised by a di usion coEa ecient D0 / e kB T , where Ea is the Figure 4.2: H is the coating thickness, arrows visually indi- activation energy corresponding to the cates the di erent components of the ux of atoms. bounding energy of atoms adsorbed in the coating and kB is the Boltzmann's constant. When desorbing light is switched on, if we assume a linear dependence on intensity IL , the di usion coecient changes Dc = D0 + d()IL

the parameter d() takes into account a wavelength dependence of the light assisted di usion. The ux of atoms leaving the coating surface is given by J + = N , where N is the atomic density in the coating and is a coecient with the dimensions of a velocity characterising the

LIAD e ect from dry- lm coating

73

desorption rate (see g.(4.2)); if is related to di usion it can be written as = 0 + a()IL

In the same way, a ux of adsorbed atoms enters the coating J = n; has the dimensions of a velocity and the ratio =vT , with vT the mean thermal velocity, represents the probability of adsorption. In the hypothesis that n is uniform in the cell, time evolution of the density in the vapour phase n(t) is then given by the di erential equation dn J + + J = dt L L is the cell length and

(n n0 )

(4.3)

1

is the characteristic time necessary to the system to go back to thermal equilibrium. On the other side, atomic density inside the coating evolves following a di usion equation @N @2N = Dc 2 (4.4) @t @x with the boundary conditions @N = (J + + J ) @x H @N Dc = 0 @x 0

Dc

(4.5) (4.6)

The last equation refers to the hypothesis that di usion from the coating to the glass of the cell walls is negligible. The system of equations (4.3)-(4.6) can be analytically solved in the limits of low and high intensity, otherwise numerical solution is necessary to compare experiment and theory [54]. As an example of the validity of this model we report a simulation of a  (t) measurement in g.(4.3).

4.3 OTS dry- lm features Dry- lm is a generic name indicating a polymer coating with a silicon-oxygen backbone terminated with a methyl group. To our knowledge there were no experimental evidences of LIAD e ect from any kind of dry- lm coating. OTS is a hydrocarbonic chain with 18 C atoms and a trichlorosilane group at one of the extremities (formula: C18 H37 Cl3 Si); at room temperature it appears as a colourless liquid and it may react with water giving also dangerous vapours if

74 6

Experimental data Simulation

5

t2

δLIAD

4 3 2 1

t1

0 100

200

300

400

500

600

Time (s) Figure 4.3: Comparison between the experimental curve and the theoretical simulation obtained with the di usion model. The red curve is the theoretical simulation, the black curve is the experimental curve referred to Rb relative density variation obtained with desorbing light intensity 6 mW/cm2 and wavelength 514nm.

inhaled. During the coating process the siloxane group chemically reacts with the silica at the surface of the glass; free Cl atoms are the product of such a reaction and a layer of hydrocarbonic chains remains on the cell walls. The preparation of dry- lm coatings requires some precautions: latex gloves should be used; the work should be done in fume hood, since the vapours of all chemicals could be dangerous, and in clean conditions. The glass cell must also be extremely clean in order to avoid formation of uncoated spots. To clean the glass we use KOH solution: 10% KOH, 45% ethanol and 45% demineralised (should be better de-ionised) water by mass. This solution should stay in the cell for 30-40 min. Then the cell is rinsed with demineralised water, then acetone, methanol and again demineralised water. After cleaning the glass cell is heated and placed under vacuum for 7-8 hours. The pressure in the cell should be about 1  10 6 Torr. If, at the end of the protocol, some white spots appear inside the cell, the procedure should be repeated. If not, the coating process can be continued. Few ml of octadecyltriclorosilane are put in a test-tube.

LIAD e ect from dry- lm coating

75

Some drops of demineralised (or de-ionised) water are then added. After a couple of minutes, a chemical reaction, which gives o bubbles of a heavy gas, takes place. The gas falls along the test-tube and enters the cell placed at the end of test-tube. The cell is rotated around to be sure that the gas di uses to all directions and the coating is uniformly distributed on the cell surface. In this phase of the process the coating on the cell's surface can not be seen by eye. The coating is ready in only few seconds. Then the cell is removed from coating area and left to stand under a fume hood for 30 minutes to allow any HCl vapours to evaporate. As last step, a methanol, demineralised water and acetic acid solution is prepared. We rst mix 95% methanol and 5% demineralised water, then we add acetic acid enough to make 5 pH solution. Then we add a 2% of the solution volume of methyltrimethoxysilane and we ll the cell and wait for 5-7 minutes. The cell is then rinsed with copious amounts of methanol and baked under vacuum at a temperature 110-120C overnight. A way to test that the coating is e ectively made, is to release one drop of water on the coated surface. The drop should move freely across the surface without wetting or leaving tracks.

4.4 Experimental set-up A sketch of our experimental apparatus is shown in g.(4.4). Atomic density in the vapour phase is monitored by absorption of a weak beam provided from a diode laser tuned on the D2 transition of Rb at 780nm; the intensity of this beam when passing through the cell is maintained under 10W in order to keep the linear behaviour of absorption, i.e. Figure 4.4: sketch of experimental setup; BE - beam expander, IF - to avoid undesired saturation efinterference lter, DL - diode laser, PD - photodiode, R - Rb reservoir. fects. Since this condition is maintained, it is possible to describe

76 the absorption in terms of the Beer's law I (x) = I0 e

2%x

= I0 e

2n(!)x

(4.7)

where % is the absorption coecient, (!) is the non-saturated frequency dependent absorption cross section and x is the length of the optical path covered by a laser beam. As we are interested in measuring LIAD (t), inverting the eq.(4.7), we obtain 

1 I0 n= ln 2(!)x I (x)

 



The data acquisition program evaluates in real time the quantity ln II(0x) by measuring I0 as the o resonance transmitted intensity and by tting each Doppler pro le of the acquired spectra to measure I (x) at the center of resonance; the two quantities (!) and x (and hence their uncertainties) are cancelled in the ratio done to obtain LIAD (see eq.(4.1)); n0 is obtained   by averaging a hundred of values of ln II(0x) before the desorbing light is switched on; from max and R. The cell we use is a cylindrical Pyrex the measured curves we are able to extract LIAD cell with a diameter of 3cm and a length of 6 cm; once the cell is coated, a capillary with a natural Rb reservoir is sealed to the cell; no bu er gas is used. Di erent light sources are used as desorbing light, in order to cover a wide spectral range from the blue-green region (Ar+ laser) to the red-near infrared region (diode lasers). A computer controlled mechanical shutter allows us to repeat the same light-dark cycles for every measurement; the shutter is closed after the atomic density reached its maximum and started decreasing: this is the typical behaviour observed in every LIAD experiment. The desorbing light is properly collimated in order to shine as uniformly as possible the whole surface of the round face of the cell.

4.5 Data analysis and discussion 4.5.1 Dependence of the LIAD e ect on the desorbing light wavelength max as a function of desorbing light wavelength while maintaining constant We have studied LIAD illumination intensity for the Rb atoms inside the OTS coated cell. As other researches on the max increases according to the desorbing photon energy and LIAD e ect have shown [62, 63], LIAD no resonance is observed as in g.4.5. It is evident that the desorbing e ect increases with the desorption frequency light. However, from the experimental data it is not clear what happens

LIAD e ect from dry- lm coating

77

4

max

δ LIAD

3

2

1

0

1

1,5

2

2,5

Photon energy (eV) max as a function of desorbing light wavelength; intensity is 6,2 mW/cm2 . Figure 4.5: LIAD

with  > 900nm. What has just been stated probably happens because the LIAD e ect could be confused with the super cial emission e ect due to the heating caused by the adsorption both of the glass and of the coating of the infrared light.

4.5.2 Multiple illumination with desorbing light One of the peculiarities of Rb density time dependence is the decrease of the Rb density after it has reached its maximum value. The decrease in density while the cell is exposed to the desorbing light indicates that LIAD depletes the coating of the adsorbed atoms. When a OTS coated cell is exposed to the desorbing light some of the Rb atoms that have been adsorbed into the coating are released. After a period of exposure to the desorbing light the ux of atoms from the coating decreases due to depletion. If the desorbing light is blocked, then subsequently

78

2,5

532nm 660nm

δLIAD

2

1,5

1

0,5

0 0

500

1000

1500

2000

2500

Time (s) Figure 4.6: Rb vapour relative density in a OTS coated cell as a function of time when the cell is repeatedly exposed to desorbing light. The red curve is obtained with the illumination condition:  =660nm, IL = 2,7 mW/cm2 . The green curve is obtained with:  =532nm, IL = 1,5 mW/cm2 ; for both curves light time is 180s while dark time between two illuminations is 240s. max is smaller if compared to the rst unblocked after a brief time (few minutes), we nd that LIAD exposure. These reasons suggest us that atomic di usion inside the coating is faster when the cell is exposed to the desorbing light than the di usion without light.

However, for a cell at room temperature if one waits few hours between exposures repeatable max are obtained. The g.4.6 shows that after each exposure,  max decreases for results for LIAD LIAD both curves; in this case we use a dark time between two illuminations of 240s while the light time is 180s: even if dark time is longer, the coating is not able to readsorb all the atoms released when illuminated; this con rm us that when the coating is exposed to the light it desorbs more atoms than the ones it adsorbed without exposure, i.e. di usion inside coating is faster when

LIAD e ect from dry- lm coating

79

max obtained with the light wavelength  = 660nm (red assisted by light. However, the LIAD curve), despite its upper light intensity, has a low decrease with respect to the exposure with light wavelength  = 532nm (green curve in g.4.6); as a matter of fact, after the rst exposures max reaches higher values. This is another evidence of the di usion dependence on the the LIAD desorbing light wavelength.

4.5.3 LIAD parameters as a function of intensity The LIAD e ect from siloxane surfaces presents a speci c behaviour with respect to the desorbing light intensity IL . We have analysed this dependence for OTS coated cells. The measurements, reported here, have been done at room temperature and the desorbing light has been supplied by an Ar+ laser tuned at 514nm. Several measurements have been carried out within an intensity max and the desorbing rate R have range of 1 - 40 mW/cm2 and for every measurement the LIAD been obtained. max as a function of intensity 4.5.3.1 LIAD max for low intensity has a linear growth; for higher intensities a bigger Data suggest that the LIAD amount of adsorbed atoms are desorbed from the coating bulk, and one could think that in the limit of I ! 1 the coating is completely depleted; so we can expect a sort of saturation in the I max trend. We have modeled such a trend with a t function of the form s(1 e I0 ); for LIAD comparison in g.(4.7) we show a t with a square root dependence, which is usually performin literature when studying LIAD from siloxane compounds; data are poorly tted by a square root function, while a better agreement is obtained by a saturation function. This can be explained with the di erent structure of OTS, that is a short polymer as compared to PDMS and paran; we plan to investigate how the structure and thickness of the coating in uence the mobility of atoms and the dynamics of the e ect. max reaches almost the same amount of desorbed The g.(4.7) shows that the OTS dry- lm LIAD atoms of the OCT and PDMS coated cells [64], but with an intensity which is around a hundred times lower. Anyway these measurements do not allow us to ascribe to the OTS compound a 100 times greater desorption eciency; their utility remains because of such a trend is not consistent with only a thermal process, due for example to a local heating of the cell walls or of the coating induced by light.

80

10

6

max

δ LIAD

8

4 Experimental data Saturating curve fit Square root fit

2

0 0

10

20

30

2

Desorbing light intensity (mW/cm ) max as a function of desorbing light average intensity; desFigure 4.7: maximum relative density variation LIAD I

orbing wavelength is 514nm, provided from an Ar+ laser; blue curve is a least 2 t with s(1 e I0 ), t p results are s = 10; 6  0:4 I0 = (17; 0  1; 2) mW/cm2 ; green curve is a least 2 t with a I , t result is p a = (1; 51  0; 05)cm= mW.

4.5.3.2 Rate R as a function of intensity A di erent trend could be observed in the initial desorbing rate R (i.e. time derivative of LIAD (t) at the instant in which light induced desorption begins), as shown in g.(4.8). Experimental data suggest a linear behaviour, the same observed in all other compounds previously studied.

4.5.3.3 Estimation of eciency max and also the slope of the R parameter cannot be used to compare As the absolute value of LIAD di erent polymers used to coat di erent cells, because of they depend on the cell construction and geometry, we have to de ne a new parameter to compare the desorption eciency of OTS

Initial desorbing rate R (Hz)

LIAD e ect from dry- lm coating

81

Linear fit Experimental data 1

0,5

0 0

10

20

30

2

Desorbing light intensity (mW/cm ) Figure 4.8: initial desorbing rate R as a function of desorbing light average intensity; desorbing wavelength is

514nm, provided from an Ar+ laser; green curve is a least 2 linear t with aI ; t result is a = (0; 0388  0; 0005)Hz cm2 /mW.

with that of other materials. If we de ne the characteristic length of the cell L as the ratio between its volume and the illuminated surface, this can be done using the parameter  = an0 L, which represent the number of desorbed atoms per incident energy unit, or equivalently with

= an0 L hc  which represent the number of desorbed atoms per incident photon. In our case L ' 3cm, n0 ' 6  109 atoms/cm3 and with the tted value of a we obtain   5; 3  1011

atoms J

 2; 1  10

7

atoms photon

which is about one order of magnitude greater of those measured with other organic coatings such as PDMS or OCT [64]. In conclusion, all the results described here, recently published [35], make OTS coating well

82 suitable for a MOT experiment.

4.6 Loading of the MOT via LIAD e ect Studies on the utilisation of a pulsed thermal source [70] demonstrate the improved eciency of pulsed loading technique. A further step, as already demonstrated [34] with PDMS, could be the fast and optically controlled release of atoms from a coated surface, giving a positive enhancement to loading eciency; we present here the rst results obtained with the Rb MOT loaded by release of atoms from a dry- lm OTS coating; further studies are necessary to understand if this technique is transportable also to the loading of traps of short lived radioactive isotopes.

4.6.1 Pulsed loading In g.(4.9) are shown two measurements performed with the \fast" version of the acquisition system, in order to acquire the maximum information from the short time evolution of the signal. In fact, we use a commercial photographic ash as desorbing light, whose duration is less than three milliseconds, shorter than all the characteristic times of the studied phenomena. It is worth noting that the time needed for the signal to go from zero to its maximum is of the order of tens of ms, which is much shorter than the characteristic loading times observed when the trap is loaded from the ionic beam (tens of seconds) or directly from the vapour by turning on the magnetic eld (a few seconds), as we saw in the preceding chapters. This demonstates the great utility of LIAD to achieve a fast trap loading. During these experiments, no Rb sources was connected to the cell, and there was no thermal di usive release of Rb from the yttrium neutraliser kept at room temperature, as it is evident from the fact that before the

ash (individuated from the spurious spike in the signal) no trapped atoms are detected. From the rate equations (1.2) with the conditions f (t) /  (t) and Nt (0) = Nv (0) = 0, in the solution (1.5) we obtain a1 = a2 , hence Nt (t) = a1 (e

k1 t

e

k2 t )

since the source term f (t) is identically zero at every time but t = 0. We can then t the acquired data with the corresponding proper curve, as shown in g.(4.10), where the t results for the

LIAD e ect from dry- lm coating

83

3

Number of trapped atoms (10 )

8 6 4 2 0

8 6 4 2 0

5

10

Time (s)

15

20

Figure 4.9: two di erent typical curves of loading the Rb MOT by illuminating the cell surface with a commercial photographic ash; rising time of the signal from zero to the maximum is of the order of tens of ms for both curves, demonstrating the faster loading process using LIAD; the spike before the trap formation is just due to the ash.

two time constants k1 and k2 are shown. Results of t are in agreement with the estimates and related considerations already discussed in sect.(1.3.2). This is a good con rmation of the validity of the model of time evolution in MOT loading and, much more important, this is the very rst demonstration of the loading of a MOT using LIAD from a dry lm coating. Further studies must be performed using a continuous illumination to desorb atoms and measure the best light parameters (wavelength and intensity) to have the best trapping eciency, as already done with PDMS coating [71].

3

Number of trapped atoms (10 )

84 2

signal fit curve

1,5

fit results: 1/k1 = (14 +/- 6) ms 1/k2 = (4,7 +/- 0,3) s

1 0,5 0 -0,5 -1 5

10

15

20

Time (s) Figure 4.10: t of a LIAD trap loading curve; the time constants k1 and k2 derived from the model described in chap. 1 are shown in the graph; tted value are reasonable value according to estimates made in sect.(1.3.2).

4.6.1.1 High collisional regime If a huge number of atoms is suddenly desorbed from the coating exposed to alkali vapour for a few weeks and never shined with intense light to deplete its bulk, we can observe a completely di erent dynamic behaviour, arising from the fact that, as already discussed in sect.(1.3.1), this is a condition where the term ANv Nt in eqs.(1.2) isn't negligible. As a con rmation of such an intense desorption, we monitor the measured pressure just after ashing on the cell, and we can see an increase of even more than one order of magnitude for a fraction of a second and a rapid restoring of the former vacuum conditions. An alternative analytic model could be proposed under the hypothesis that the mentioned term is not only not negligible, but even dominant, and, due to the fact that the number of desorbed atoms in the vapour phase could be thought as very big, the number of trapped atoms is negligible with respect to it, so the evolution of Nv

LIAD e ect from dry- lm coating

85

3

Number of trapped atoms (10 )

200 Experimental data Fit curve 150

100

50

0 10

5

15

20

Time (s) Figure 4.11: trap loading in a high collisional regime; the di erent behaviour with respect to g.(4.10) is evident. is independent to that of Nt , hence Nv (t) = N0 exp ( t= ); under this conditions we can write N_ t = ANt N0 exp t= + LN0 exp ( t= )

which admits a solution of the form Nt (t) =

L h H (e( e A

t= ) 1)

eH (e

( t= ) e(t= ) )

i

where H = N0 A , and  represents a characteristic time of evolution of the phenomenon. In g.(4.11) is reported such a signal with the corresponding t curve, showing on a 20 s time scale, the validity of the proposed model; for longer times in fact, the linear collisional term CNt becomes competitive with the non linear one, and is the main responsible to the number of trapped atoms going to zero. Result of t gives  = (8; 4  0; 7) s, which is longer than any other characteristic time of our trap experiments, demonstrating the di erent and complex dynamics

86 involved in such conditions. Unfortunately, such a high collisional regime is not reproducible on a day to day operation, because the coating need to be exposed to thermal Rb vapour for a few weeks before obtaining again a similar curve, hence a further studies on this particular MOT loading regime are not easy to realize.

8

3

Number of trapped atoms (10 )

140 6

120

4 2 0

100

-2 0

5

10

15

20

80 60 40 20 0

100

200

300

400

500

Time (s) Figure 4.12: after each ash, the number of trapped atoms increases; in the inset is shown a measurement with no background trap, made just before the one in the main plot; sudden losses and recoveries of signal are due to Ti:Sa laser instabilities.

4.6.2 Increasing of number of trapped atoms via non alkali desorption A positive e ect on the trap signal due to an illumination on the cell with a ash, is measurable even when Rb is no more desorbed from a completely depleted coating; in these conditions we observe anyway a pressure increase after shining the cell with an intense light in spite of no

LIAD e ect from dry- lm coating

87

trap signal is measured (see inset in g.(4.12)): this means that other elements or molecules or the coating itself are released in vapour phase. In g.(4.12) it is possible to observe the growth of the trap population after each ash; such a \background" trap is loaded from the thermal release of Rb from yttrium catcher. It is quite surprising that an increase in the rest gas pressure could result in a better trapping eciency; this counterintuitive e ect is not yet well understood, but can be explained as a sort of bu er gas loading. Such e ect should not be interpreted as the one already observed in other types of trapping experiment [72, 73], where an ultracold gas is used to thermalise the particles at few hundreds of K using collisions. In our rate equation loading scheme, we can interpret the experimental result with a reduction of the mean thermal velocity and increasing of interaction time of the atoms due to collisions with the molecules desorbed from the coating; in many experiments requiring long lived atomic polarisation coherence (see for example [74]) the same e ect of time of ight enhancement due to bu er gas is used to narrow the linewidth of atomic resonances. In other words, that is a sort of pre-cooling, before atoms enter the trap from the vapour phase. Unfortunately, pressure increase of the collisional rate C is in contrast with this e ect, thus it seems dicult to obtain a dramatic improvement in trap population; in g.(4.12) only a factor of 3 is achieved. Another interesting feature is that the characteristic time of evolution in the process is longer of any other distinctive time scale of our MOT. This can be explained if we suppose that desorbed molecules are much more massive and then much slower than Rb atoms in the cell. Further studies are hence necessary to understand if this e ect can be e ectively used in a MOT experiment.

Chapter 5

Conclusions and outlook That's a great plan, Walter. That's fuckin' ingenious, if I understand it correctly. Je rey Lebowski (1998)

In this dissertation have been presented and discussed the recent results of the TRAPRAD collaboration concerning magneto optical trapping of francium isotopes (the only francium MOT active experiment at the moment in the world), and of the experiments carried out at the Department of Physics of Universita degli Studi di Siena concerning light induced atomic desorption from dry lm coating, as a possible development and improvement for TRAPRAD itself. After the implementation and testing on a Rb MOT of a very high sensitive acquisition system, able to detect a cloud of even a few tenths of atoms, images and data on the francium trap have been acquired, leading to a maximum number of about 8000 trapped atoms in pulsed regime; di usion features of francium has been measured using the time dynamics of the trap loading process; trapping eciency was also estimated to be less than 10 3 . Concerning a possible improvement of this result, we study and demonstrate (up to now only with rubidium atoms) the possibility of loading the MOT via Light Induced Atom Desorption from a dry lm coating of the cell walls; LIAD was for the rst time observed from this type of organic compound; in

Conclusions and outlook

89

Figure 5.1: scheme of trapping and repumping 7P levels, and 6D levels; lifetimes are indicated as well as transition wavelengths.

particular we studied and measured the LIAD features and parameters of OTS coating, as well as the rst MOT loading signals. The aim of this last chapter is to discuss about the possible short and long term perspectives of the francium MOT facility at L.N.L.

5.1 Energy of the 6D level From a theoretical point of view, atomic structure of francium is extensively studied; in ref. [75] it is possible to nd tabulated many energies of francium levels; thanks to ISOLDE collaboration rst and Orozco's group in the last decade, energies of rst excited levels [22] have been also experimentally determined, but the knowledge of this atom remains still under investigation. We plan to measure the energy of 6D level, whose wavelengths are predicted to be, according to [75], 608 nm for the 6d5=2 and 616 nm for the 6d3=2 term. These wavelengths are quite easily accessible with a rhodamine dye laser (the same type used for Na spectroscopy and trapping). The choice of this transition lies in the fact that, due to angular momentum selection rules, it

90 is electric dipole forbidden, while electric quadrupole allowed; this makes this weak transition a very good training for a possible measure of the parity violating transition 7S-8S. If we look at the level scheme in g.(5.1), due to predicted long lifetimes for the 6D levels (2200 s or the 6d5=2 and 640 s for the 6d3=2 term, compared with less than 30 ns for the 7P levels), an atom excited from the ground state exits the trapping repumping transitions cycle, and then, at resonance, we expect a depletion of trap signal. It is possible to estimate from a two level atomic theory, that the probability transition in an 2 , with the ne structure electric quadrupole transition is depleted of a term of the order FS FS constant, with respect to an electric dipole transition; thus the saturation parameter is increased of about 4 orders of magnitude (approximatively the value of FS2 ) with respect to the 7S-7P transition in this rough estimate. Finally, to get saturation in performing spectroscopy on the 6D level, we have to achieve an intensity of the order of less 100 W cm 2 , which is well feasible with a proper designed optical system. In the region of the MOT (about 1 mm in diameter) is then enough to focus a total power of about 250 mW to perform saturation spectroscopy or even less to remain in a linear absorption regime. Installation of the dye laser in the laser room at L.N.L. is scheduled before the end of 2007 and next beam times will be devoted to measure the wavelength of the 7S-6D transitions.

5.2 Towards APV measurements Possible ways and problems in an APV measurements in francium atom has been widely discussed in [76, 77]. We report here a brief outline of the subject and of the diculties in such a measure in a cold cloud of atoms. The parity violating transition is the highly forbidden 7S-8S at 506 nm. First of all let's consider the amplitude probability for the transition, which is given from the expression of the e ective dipole ~ d~e  ^ E~ + M10 ~ ^ ~k iIm(E1P V )~ F;F 0 = E i ~ where E~ is an external applied electric eld necessary to make the transition slightly allowed, ~ are the Pauli's matrices, ~k is the wave vector of the laser light, M10 = M1 + M1hf (F 0 F ) represents the magnetic dipole moment and E1P V is the amplitude of parity violation; nally and represent here the scalar and vectorial polarisability. The quantities ; and M1 are

Conclusions and outlook

91

theoretically calculated [78, 79] = ( 375; 3  3; 6)a0 3

= (74; 3  0; 7)a0 3

M1 = 46(1  16%)  10

5

jB =cj

while the calculation for the parity violating term gives Im(E1P V ) = ( 1; 33  0; 02)  10

10 ea 0

with a0 the Bohr's radius, e the proton charge and B the Bohr's magneton. As APV measures the change in the excitation rate of such a transition when a mirror symmetry is applied to the system (the external electric eld is reversed for example), precise knowledge of all the terms in the e ective dipole expression is needed before measure APV directly. A possible preliminary measurement could be the ratio ; in cesium atom this has been already made in an atomic beam [80], giving a good agreement between theory and experiment; a possible similar approach to the same measurement on francium is outlined in [81]. Such an experiment performed in our system would be the rst of this type on francium and also in a cold sample. A possible approach could be the following: for linear polarisation of the laser parallel to the electric eld we obtain an excitation rate proportional to 2 E 2 , while, neglecting the term M proportional to M10 (for example with E = 1000 V cm 1 we have 1 ' 0; 12), for orthogonal E polarisation the rate is proportional to 2 E 2 . Another possibility is to use circular polarisation, giving an excitation rate proportional to (  )2 E 2 with the sign depending on the ellipticity. Di erently from the case of the 6D level, radiative lifetime of 8S level is predicted to be of the order of 60 ns [75], so after excitation, in a time too short to observe an e ect in the trap population, the atom enter again in the trap and repump cycle. A possibility to achieve a signal related to the excitation rate comes from the fact that ionisation energy from 8S is about 1,6 eV, while the photon energy at 506 nm is about 2,4 eV; if the cross section for photoionisation process is high enough to depopulate the trap, the measure of the ratio becomes possible with such a scheme; hence an accurate theoretical study of the problem is necessary, to understand the amplitude of the expected signal.

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