Broadband Vibrational Cooling of Cold Cesium Molecules: Theory and Experiments

CHINESE JOURNAL OF CHEMICAL PHYSICS VOLUME 22, NUMBER 2 APRIL 27, 2009

ARTICLE

Broadband Vibrational Cooling of Cold Cesium Molecules: Theory andExperiments†

D. Sofikitisa, A. Fiorettia∗, S. Weberb, M. Viteaua, A. Chotiaa, R. Horchania, M. Allegrinia,c, B. Chatelb,D. Comparata, P. Pilleta∗

a. Laboratoire Aime Cotton, CNRS, Universite Paris-Sud, Bat. 505, 91405 Orsay, Franceb. Laboratoire Collisions, Agregats, Reactivite (UMR 5589, CNRS-Universite Paul Sabatier Toulouse 3),IRSAMC, Toulouse, Francec. CNISM, Dipartimento di Fisica, Universita di Pisa, Largo Pontecorvo, 356127 PISA, Italy

(Dated: Received on January 24, 2009; Accepted on March 23, 2009)

The use of a broadband, frequency shaped femtosecond laser on translationally cold cesiummolecules has recently demonstrated to be a very efficient method of cooling also the vi-brational degree of freedom. A sample of cold molecules, initially distributed over severalvibrational levels, has thus been transfered into a single selected vibrational level of thesinglet X1Σg ground electronic state. Our method is based on repeated optical pumpingby laser light with a spectrum broad enough to excite all populated vibrational levels butlimited in its frequency bandwidth with a spatial light modulator. In such a way we areable to eliminate transitions from the selected level, in which molecules accumulate. In thispaper we briefly report the main experimental results and then address, in a detailed way bycomputer simulations, the perspectives for a “complete” cooling of the molecules, includingalso the rotational degree of freedom. Since the pumping process strongly depends on therelative shape of the ground and excited potential curves, ro-vibrational cooling throughdifferent excited states is theoretically compared.

Key words: Cold molecule, Optical pumping, Pulse shaping, Ultrashort pulse, Laser cooling

I. INTRODUCTION

The manipulation of atomic or molecular quantumdynamics and the availability of robust and selectivemethods of performing population transfer in quan-tum systems is essential for a variety of fields, such asprecision spectroscopy, quantum computing, control ofmolecular dynamics and chemical reactions [1-4]. Inparticular, the activities developed in the domain ofcold molecules through precise control of both inter-nal and external degrees of freedom of a molecule areexpected to lead significant advances in collision dy-namics of chemical reactions, molecular spectroscopy,molecular clocks, fundamental test in physics, con-trolled photo-chemistry studies, and quantum compu-tation with polar molecules [5-10].

During the last two decades important technologi-cal breakthroughs opened the possibility of obtainingarbitrarily shaped optical waveform in the fs-ps do-main. This has led important results in coherent control[11-13], compression of optical pulses [14], and optical

†Part of the special issue for the “4th Sino-French Workshop onMolecular Spectroscopy, Dynamics and Quantum Control”.∗Authors to whom correspondence should be addressed. E-mail:[email protected], [email protected]

communications [15]. These pulse shaping techniques,which permit to control the phase as well as the ampli-tude of each spectral component of the laser pulse, havebeen reviewed in details [16]. There have been someproposals to manipulate the internal degree of freedomof molecules using such phase and amplitude techniques[17-20]. In the experiments described in this work, thistechnique is employed to achieve the vibrational cool-ing of molecules into selected vibrational levels usingamplitude shaping only.

An experimental realization of the vibrational cool-ing based on optical pumping using a train of severalidentical weak femtosecond laser pulses have been re-cently published [21]. Cs2 molecules initially formedvia photoassociation (PA) of cold Cs atoms in severalvibrational levels, v, of the electronic ground state wereredistributed in the ground state via a few electronicexcitation-spontaneous emission cycles by applying afemtosecond broadband laser. The laser pulses wereshaped to remove the excitation frequency band of thev=0 level, thus preventing “excitation from” and lead-ing to an efficient “accumulation into” this lowest vibra-tional level of the singlet ground state. Subsequently,using the flexibility of femtosecond pulse shaping tech-niques [22], this population pumping method has beenextended in order to accumulate molecules into a singleselected vibrational level other than the v=0 one [23].

DOI:10.1088/1674-0068/22/02/149-156 149 c©2009 Chinese Physical Society

150 Chin. J. Chem. Phys., Vol. 22, No. 2 D. Sofikitis et al.

Here, we present a survey of these experimental resultstogether with a more detailed theoretical analysis.

In this work, we first recall the principle populationtransfer from several energy eigenstates into the low-est vibrational level in the case of the cesium dimer.We then briefly describe our experimental apparatus inits main parts: the magneto-optical trap (MOT) wherethe cold molecules are produced and the pulse shapingapparatus based on a liquid crystal spatial light modu-lator (LC-SLM) placed in the Fourier plane of a highlydispersive 4f line [24]. Then we describe our experi-mental results: the selective vibrational cooling of themolecules into a given vibrational level on demand. Ex-amples are reported for v=0, v=1, v=2, and v=7. Fi-nally, we analyze in detail the possibilities of a very largeband vibrational cooling as well as those for rotationalcooling, showing the dependence on the particular ex-cited potential curve chosen for the pumping process.

II. LASER COOLING OF THE MOLECULARVIBRATION

A. Optical pumping

The main idea in the vibrational optical pumping asperformed in Refs.[21,23], is to use a broadband lasertuned to transitions between the different vibrationallevels of the molecule, which we label vX and ve, be-longing respectively to the singlet-ground-state X1Σg,hereafter simply referred as X, and to an electroni-cally excited state, for instance either the B1Πu or theC1Πu states of the Cs2 system, hereafter referred sim-ply as B or C. The goal is to start from a given vi-brational distribution of vX values, as obtained afterthe PA, and to transfer it into a single targeted vX

level. The absorption-spontaneous emission cycles lead,through optical pumping, to a redistribution of the vi-brational population into the ground state according tothe scheme:

Cs2(vX) + hνlas −→ Cs2(ve) −→ Cs2(v′X) + hνem (1)

where hνlas and hνem are the energies of the laser andof the spontaneously emitted photons respectively. Thebroadband character of the laser allows repetition of thepumping process from multiple vibrational vX levels.By removing the laser frequencies corresponding to theexcitation of a selected vX level, we prevent molecules tobe pumped out of it, thus making this level a dark state.As time progresses a series of absorption-spontaneousemission cycles described by Eq.(1), leads to an accu-mulation of the molecules into the selected vX level.

B. Cold molecule production

The initial cold molecule formation is achieved ina Cs vapor-loaded MOT via photoassociation, a pro-cess where two atoms resonantly absorb a photon to

create a molecule in an excited electronic state thatcan decay into stable deeply bound vibrational lev-els of the singlet molecular ground X state. Detailson the experimental setup and methods can be foundin Refs.[21,23,25] and in references therein. The lasertransitions used are summarized in Fig.1 together withthe relevant potential curves. PA is achieved using acw Titanium:Sapphire laser (intensity of 300 W/cm2)pumped by an Ar+ laser. This laser is red-detuned byroughly 2 cm−1 with respect to the 6s→6p3/2 atomictransition, resonant with an excited molecular level. Af-ter spontaneous decay, the distribution of the moleculesspans the v=1-10 levels of the X ground state. Detailsof this PA mechanism are in Ref.[25].

These stable molecules are then ionized by resonantlyenhanced multiphoton ionization (REMPI) throughthe excited C1Πu molecular intermediate state. TheREMPI detection uses a pulsed dye laser (wavenumber∼16000 cm−1, spectral bandwidth 0.1 cm−1) pumpedby the second harmonic of a pulsed Nd:YAG laser (repe-tition rate 10 Hz, duration 7 ns). The formed Cs2+ ionsare detected using a pair of microchannel plates througha time-of-flight mass spectrometer. By scanning theREMPI laser wavelength the experimental spectrumis monitored. The observed lines represent transitionsfrom vibrational ground levels vX=1-10 level to variouslevels vC of the C state and have been assigned [21,25]using the spectroscopic study of Ref.[26]. Any redis-tribution of population among the vibrational levels ofthe ground state introduced by some additional laser

FIG. 1 Potential curves for the cesium dimer relevant for theexperiment. Cold atoms are excited at long range by the PAlaser into a molecular excited level that subsequentely decaythrough two spontaneous emissions into a stable moleculein a vibrational level of the ground X state. The shapedfemtosecond laser pumps the produced molecules, via theintermediate excited B state, into a single selected vibra-tional level of the X state. Molecules are finally selectivelyionized by two-step REMPI ionization via the intermediateexcited C state. In the simulations, the C state is also usedas intermediate state for optical pumping.

DOI:10.1088/1674-0068/22/02/149-156 c©2009 Chinese Physical Society

Chin. J. Chem. Phys., Vol. 22, No. 2 Broadband Vibrational Cooling of Cold Cs2 Molecules 151

light results in a clear change in the relative intensitiesof the lines present in the spectrum. The moleculardistribution among different levels can thus be moni-tored [21,23]. On the contrary, the low resolution ofthese REMPI spectra do not provide, at present, thecapability of analyzing the rotational distribution of themolecular sample.

In our experiment, a shaped femtosecond laser pulseis used to achieve vibrational cooling. It is providedby a Kerr-Lens-Mode-locking Titanium:Sapphire oscil-lator with a repetition rate of 80 MHz (12.5 ns betweensubsequent pulse). The central wavelength is tunedat 773 nm. Its spectral full width at half maximum(FWHM) is around 10 nm. The shaping is obtained byblocking part of the frequencies present in the femtosec-ond laser pulse with a LC-SLM in the Fourier plane, asdescribed in the following.

C. Pulse shaping

In order to control the optical pumping, the spectrumof this femtosecond laser is shaped by a high resolu-tion pulse shaper [24]. This one is composed of a dualLC-SLM placed in the Fourier plane of a folded zerodispersion line (see Fig.2) which allows phase and am-plitude modulation [27]. The LC-SLM (Jenoptik, SLM-S640/12) possesses 640 pixels and has been described inRef.[28] (stripes of 97µm×10 mm separated by gaps of3 µm).

The regions of liquid-crystal between the patternedelectrodes cannot be controlled and are referred to asgaps. In these gap regions the liquid-crystals behave ina first approximation as though there were no appliedvoltage so that the filter for the gap regions is assumedto be constant across the array. This limits the on-offratio (extinction ratio) to the theoretical value of 20 dB(1% intensity extinction). Using an OCEAN Optics HR4000 spectrometer, we have measured an on-off ratio of3% of the light intensity in the worse case, probablydue to imperfect experimental polarization. Thus, inthe simulations of the experiment this 3% conservativevalue is taken as the reference.

To avoid chromatic as well as off-axis aberrations,the setup reported in Fig.2 is chosen. The beam is firstdispersed by a gold-coated grating with 2000 lines/mmand then focused in the horizontal plane by a cylindri-cal mirror with a focal length of 600 mm in the Fourierplane. The two LC-SLM (64 mm in width) are placedin the Fourier plane just behind the ended mirror whichallows to fold the line without any misalignment effectthanks to the large Rayleigth length. In this design,the beam passes twice in the dual LC-SLM. By con-struction, this setup provides a perfect symmetry of thezero-dispersion line which simplifies greatly the align-ment procedure. The central wavelength of the 4f-lineis set to 773 nm.

These characteristics provide an average resolution of

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FIG. 2 Experimental setup for the pulse shaper and thecold molecule production and detection. Upper part: foldedzero dispersion line. The beam is dispersed by the grating Gand then each spectral component is spatially separated andfocused by the cylindrical mirror CM in the Fourier plane.FM is a plane folding mirror. Both LC-SLMs (detailed inthe lower left side of the figure) are at the Fourier plane.An end mirror EM is placed just after the LC-SLM and thebeam goes twice through the half of the line. The shapedlight is then sent through the cold molecular cloud that iscreated by PA (with a cw laser) of an atomic Cs cloud cooledby a standard 6 beams vapor-loaded MOT. The moleculesare then detected using a REMPI ionization laser creatingCs2

+ ions, which are accelerated by an electric field createdwith the two grids surrounding the cloud, and monitoredusing a pair of micro-channel plates.

0.06 nm/pixel and is able to shape a spectral width of38 nm, which is large enough to transmit the spectralpedestal width of our laser source (FWHM of 10 nm).The sagittal beam FWHM in the Fourier plane (57 µm,corresponding to an input beam diameter of 2.3 mm) isroughly set to the width of a pixel, therefore maximizingthe resolution of the pulse shaper. The setting timeinherent to these liquid-crystal device (20 ms) does notrepresent a limitation for this experiment because theLC-SLM configuration was not changed within a singlespectrum.

In the present experiment an average laser power ofonly 3 mW is used and focused on the molecular cloudwith a waist of nearly 500 µm, corresponding to anintensity of 700 mW/cm2. A similar value is used inthe simulations.

D. Theoretical modelling

In order to predict the best possible laser spectrum,we have modeled the optical pumping in a very simple



FIG. 3 Left part: the experimental pulse spectra used to cool the vibrational distribution into the vX=0 (a), vX=1 (b),vX=2 (c), vX=7 (d), and vX=1 (e) levels respectively. Right part: the corresponding experimental ionization spectrashowing mainly transition involving only the selected levels, instead of the very rich spectrum of Refs.[21,25], reported forclarity in (f). Notice that in the spectrum (c) a small signal corresponding to molecules in the vX=0 remains, and that inthe spectrum (d) molecules in the vX=1 level also remain. In (e) the excitation spectrum contains only a few frequencies,calculated in order to pump molecules in an optimal way to vX=1. In (f), where the femtosecond laser is not present, allobserved peaks can be assigned to specific vX→vB transitions. For interpretation of the color in this figure legend, thereader can refer to the web version of this article.

way. Using the known X, B, and C potential curvesand their rotational constants [29,30], we calculate thero-vibrational energy levels as well as the Frank-Condon(FC) factors for the transitions. Because of the very lowaverage laser intensity we are in a perturbative regime.Thus, we could assume that the excitation probabil-ity is simply proportional to the laser spectral densityat the transition frequencies, the FC factor, and theHonl-London factor. If needed, rate equations couldbe determined, and solved exactly using kinetic MonteCarlo modeling [31]. As less than one photon is ab-sorbed during the excited state lifetime (∼15 ns), wesimply assume total population decay before sending,12.5 ns later, another broadband light pulse. Initially,in each simulation, the molecules lie in the levels vX=1to 10, with a distribution measured experimentally inRef.[21]. The femtosecond laser spectrum needed to re-alized such dark state is first theoretically calculated,utilizing the results of Ref.[26], and then implemented,using the pulse shaper, into a real spectrum.

Other processes, like 3-photons direct ionization bythe femtosecond laser or predissociation, are estimatedto be not relevant for the experiment and are not takeninto account by the simulation.

III. EXPERIMENTAL RESULTS

In the first experiment, presented in Fig.3(a), we useour LC-SLM setup to recover the result already pre-sented in Ref.[21] where the shaping was simply real-ized by placing a razor blade in the Fourier plane [32]of a 4f-line. For the cesium dimer, the frequencies thatcorrespond to excitation of the ground vibrational levelvX=0 to any vibrational level of the B potential liehigher than a 13000 cm−1 threshold. Consequently, therequired laser shaped spectrum is simply the usual laserspectrum truncated at this threshold. The ionizationspectrum clearly shows that all transitions correspond-ing to ground levels other than vX=0 disappeared, whilethose corresponding to the vX=0 level are strongly en-hanced.

The idea of removing the frequencies that correspondto (all) possible excitations of a particular vibrationallevel, in order to form a dark state where molecularpopulation can be accumulated by optical pumping, canbe applied not only to the vX=0 level but to a numberof selected levels.

The generality of the method is demonstrated by se-lecting other vibrational levels, for instance the vX=1,



vX=2 and the vX=7 target states, shown in Fig.3 (b),(c), and (d) respectively. For each chosen target vX , theionization spectrum contains mainly lines in positionscorresponding to transitions from the selected levels toseveral excited vibrational levels.

In principle, any vibrational level can be chosen asthe target state. The obvious limitation lies upon theavailable laser bandwidth and upon the initial moleculardistribution. The laser has to be strong enough in thevicinity of transitions between the initial states and thetarget one.

In this section it has been demonstrated that a greatpart of the molecular population initially present canbe transferred to a desired vibrational level when thefrequencies that connect it to any of the excited statesused in the optical pumping scheme, are removed fromthe shaped femtosecond pulse. However, the efficiencyof such an optical pumping procedure depends on var-ious parameters: the FC factors, i.e. of the relativeposition of the electronically excited potential with re-spect to the ground potential, the bandwidth of thefemtosecond pulse used and the extinction ratio of thepulse shaper.

The efficiency of these and other vibrational coolingprocesses can be estimated theoretically through com-puter simulations, which make the object of the follow-ing section.

IV. PERSPECTIVES FOR VIBRATIONAL ANDROTATIONAL LASER COOLING

A. Very large broadband cooling

The computer simulations of the vibrational coolinginto the v=0, 1, 2, and 7 with the method describedas above were shown in Refs.[21,23]. Using a parameterset (laser intensity and spectrum, SLM extinction ratio,initial vibrational distribution) that mimics experimen-tal conditions, our calculations show that, for the vX=0case, after 104 pulses nearly 70% of the initial popula-tion is transferred into the target level. In the vX=1case, after the same number of pulses, only 53% of thepopulation is transferred [23]. Experimental data showa qualitative agreement with this calculated efficiency.

This incomplete transfer depends mainly on two ef-fects: the limited bandwith of the femtosecond laserand the non-zero extinction ratio of the LC-SLM. Whenmolecules are pumped by excitation-spontaneous emis-sion cycles, depending on the specific FC values, theycan decay also into higher lying vibrational levels, wherethey become less and less resonant with the laser light,until they finally exit the cooling process and remainunaffected by the femtosecond laser. This process ispictorially represented in Fig.4(a). Molecules, for in-stance in vX=10, are laser excited to a vB level (thickgreen arrow to vB=7 in Fig.4(a)), which has a rela-tively large FC factor and lies within the bandwidth

of the laser (case with both grey shade and red lines).They subsequently decay mainly where the FC factorsare more favorable (green dotted arrows in Fig.4) andthus produce either lower or higher vibrational levels(in this case vX = 3 and vX=14). When the next laserpulse arrives the process is repeated but, due to limitedbandwidth of the laser, while the vX=3 molecules arewith high probability finally pumped towards the tar-get vX=0 level, the vX=14 are mainly pumped furtheroutwards and quickly lost for the pumping process.

On the other side, the unperfect extinction ratio, pre-dominant in the vX=1 case, depends on the residual3% of laser light resonant with transitions from the tar-get level, which has the deleterious effect of pumpingmolecules out of this no-more dark level. If a broad-band laser and a perfect extinction ratio are used in thesimulations, a nearly 100% efficiency is obtained.

B. Rotational cooling

Concerning the possibility of cooling also the rota-tional degree of freedom, it is worthwhile to note that,for the Cs dimer in the X state, the resolution requiredin order to separate all rotational levels would be in theorder of 0.01 cm−1 (corresponding to 0.6 pm), whichis difficult to be achieved experimentally and beyondthe capabilities (∼0.06 nm) of the present pulse shaper.However, we would like to demonstrate with our simu-lation that rotational cooling is indeed in principle fea-sible by studying the simple possible case of populationtransfer toward the lowest ro-vibronic state of the Cs2molecules, namely vX=0-JX=0 level, where JX repre-sent the rotational quantum numbers in the X state.

A natural possibility for laser cooling the molecularrotation is to shape the laser by removing the frequen-cies corresponding to the transitions ∆J=Je−JX=0,+1 (Q and R bands), where Je and JX repre-sent the rotational quantum numbers in the excitedand ground levels respectively, and leave only the∆J=Je−JX=−1 (P band) ones that are J lowering(except the JX=1→Je=1 that is needed to empty theJX=1 level). With such a shaping, absorption- sponta-neous emission cycles would indeed lead to a decreaseon average of the principal rotation quantum numberJX , i.e. to laser cool the rotation. Figure 4(d) showsthe evolution of the rotational quantum number duringthe vibrational cooling towards vX=0. As it is evidentfrom Fig.4(d), the spread of rotational quantum numberincreases with time. This behavior can be understoodfrom the Fig.4(c), where are represented the energiescorresponding to the rotational transitions between thevibrational levels vX=0 and vB=0. As it is impossi-ble to remove all above mentioned “bad” ro-vibrationaltransition with a simple cut in the frequencies (repre-sented by the dashed horizontal cut in the figure), itturns out that the B state is simply not a good can-didate to perform rotational cooling. The only possi-



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FIG. 4 Simulation for the ro-vibrational cooling with a truncated spectrum through the excited B state: (a) FC factorsfor the X-B transitions (grey levels), the red lines indicate the energy range covered by the truncated (allowed frequenciesv ≤13000 cm−1) laser spectrum, green arrows are explained in the text; (b) temporal evolution of the vibrational populationwhen using the pulse in (a); (c) energy structure of the P, Q, and R bands (∆J=−1, 0, +1 respectively) for the vX=0-vB=0transitions, the green line represents an hypothetical cut in the laser spectrum; (d) temporal evolution of the rotationalpopulation of the vX=0 level. For interpretation of the color in this figure legend, the reader can refer to the web version ofthis article.

bility would be to remove selectively all the undesiredfrequencies one by one, which is not experimentally fea-sible because the spectral resolution of our LC-SLM inthe present configuration is too low.

The other electronically excited potential curves thatcan be considered for ro-vibrational cooling is the Cstate. The X→C transitions lay in the energy rangenear 16000 cm−1, which is unfortunately out of reachfor our femtosecond laser (10000-14300 cm−1) but couldbe attained, for instance, by a laser diode. The struc-ture of the FC factors (Condon parabola) is such thatvibrational cooling is possible even without shaping thepulses, as can be seen in Fig.5(b), although with a mod-erate efficiency (nearly 45%). Although it is appar-ent (see Fig.5(d)) that bare pulses do not cool rota-tion, the energy structure of the ro-vibrational transi-tions (P, Q, and R bands) shows that the transitions∆J=JC−JX=0 can be easily suppressed by a simpleenergy cut, provided the energy resolution is sufficient(see Fig.5(c)). Furthermore the high FC value betweenvX=0 and vC=0 ensures that no spurious heating couldoccur by population transfer to vX 6=0 levels.

Finally, Figure 6 shows the results of a simulation

where the molecules are simultaneously vibrationallyand rotationally cooled by applying the excitation to-wards the C state. This process theoretically works finebut may be too complicated to realize experimentally.The pulse shown in Fig.6(c) has a cut in frequencies thateliminates the Q and R bands (except the JX=1→Je=1transition) and is shaped in such a way to pump themolecular vibration in an optimal way [23] with a set offrequencies the molecular vibration (like in Fig.3(e)).

Another possibility that gives promising results whilebeing experimentally feasible, is to cool the vibrationby pumping through the B state and the rotation bypumping through the C state, as proposed in Ref.[23].In this case the rotation is cooled by using a spectrumtruncated in energy as in Fig.5(c), while the vibrationis cooled with a femtosecond pulse shaped by the LC-SLM. Obviously such a scheme would require an exter-nal broadband source to excite the X state moleculestowards the C state. A possibility is to use a simplebroadband diode laser near 627 nm.



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FIG. 5 Simulation for the ro-vibrational cooling with an unshaped spectrum through the excited C state: (a) FC factorsfor the X-C transitions (grey levels), the red lines indicate the energy range covered by the laser spectrum; (b) temporalevolution of the vibrational population when using the pulse in (a); (c) energy structure of the P, Q, and R bands for thevX=0→vC=0 transitions, the green line represents an hypothetical cut in the laser spectrum; (d) temporal evolution of therotational population of the vX=0 level. For interpretation of the color in this figure legend, the reader can refer to the webversion of this article.

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FIG. 6 Simulation for the ro-vibrational cooling with a complex shaped spectrum through the excited C state: (a) FC factorsfor the X-C transitions (grey levels), the red lines indicate the energy range covered by the laser spectrum; (b) temporalevolution of the vibrational population; (c) theoretical shaped spectrum of the broadband laser; (d) temporal evolution ofthe rotational population of the vX=0 level. For interpretation of the color in this figure legend, the reader can refer to theweb version of this article.



V. CONCLUSION

We have studied experimentally how femtosecondpulse shaping techniques can be used to realize effi-cient vibrational cooling by optical pumping of cold Cs2molecules. The method demonstrated here is based on alight source spectrally broad enough to excite all popu-lated vibrational levels and shaped in amplitude in sucha way to eliminate all frequencies that could excite thedesired target vX=0 level. With an appropriate pulseshaper, we have demonstrated the optical pumping tosingle vibrational levels such as v=0,1,2 and v=7. Theefficiency of the optical pumping is mainly limited bythe finite laser spectral bandwidth and the imperfectextinction ratio of our LC-SLM. In principle, the the-ory indicates that the use of broader sources and betterextinction ratio would allow up to 100% transfer of pop-ulation in one single vibrational level.

We have then studied, by means of computer simu-lations, the possibility to cool also the rotational de-gree of freedom. Rotational cooling can in principle beperformed in a similar way provided the laser band-width and the experimental ability to shape the lasermatch the rotational energy spread. The experimen-tal feasibility depends strongly on the choice of the ex-cited state used for optical pumping. We theoreticallydemonstrated that the C state is a good candidate tocool the rotation in the v=0, J=0 level.

This experimental demonstration of vibrational cool-ing and the good perspectives for the rotational oneopen the way to possible schemes for direct laser cool-ing of molecules [33,34]. Eventually, accumulation ofmolecules in an optical trap could lead to study of colli-sional processes in order to assess the efficiency of evap-orative cooling or to investigate ways for achieving con-trolled chemistry.

VI. ACKNOWLEDGMENTS

This work was supported by the Institut Franciliende Recherche sur les Atomes Froids (IFRAF) and (inToulouse) by the Agence Nationale de la Recherche(Contract ANR-06-BLAN-0004) and the Del Ducafoundation.

M. Allegrini thanks the EC-Network EMALI and(Galileo Project) Universite Franco-Italienne. Wethank Nadia Bouloufa and Olivier Dulieu for providingus with the FC calculations.

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Broadband Vibrational Cooling of Cold Cesium Molecules: Theory and Experiments

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Transcript of Broadband Vibrational Cooling of Cold Cesium Molecules: Theory and Experiments