Velocity preserving transfer between highly excited atomic states: Black Body Radiation and Collisions
J.C. de Aquino Carvalho, I. Maurin, H. Failache, D. Bloch, A. Laliotis
VVelocity preserving transfer between highly excited atomic states: Black BodyRadiation and Collisions
J.C de Aquino Carvalho,
1, 2
I. Maurin,
1, 2
H. Failache, D. Bloch,
2, 1 and A. Laliotis
1, 2, ∗ Laboratoire de Physique des Lasers, Universit´e Paris 13,Sorbonne Paris-Cit´e, F-93430, Villetaneuse, France CNRS, UMR 7538, LPL, 99 Avenue J.-B. Cl´ement, F-93430 Villetaneuse, France Instituto de Fısica, Facultad de Ingenierıa, Universidad de la Republica,J. Herrera y Reissig 565, 11300 Montevideo, Uruguay (Dated: January 21, 2021)We study the excitation redistribution from cesium 7P / or 7P / to neighboring energy levelsby Black Body Radiation (BBR) and inter atomic collisions using pump-probe spectroscopy insidea vapor cell. At low vapor densities we measure redistribution of the initial, velocity-selected,atomic excitation by BBR. This preserves the selected atomic velocities allowing us to perform highresolution spectroscopy of the 6D →
7F transitions. This transfer mechanism could also be usedto perform sub-Doppler spectroscopy of the cesium highly-excited nG levels. At high densities weobserve interatomic collisions redistributing the excitation within the cesium 7P fine and hyperfinestructure. We show that 7P redistribution involves state-changing collisions that preserve the initialselection of atomic velocities. These redistribution mechanisms can be of importance for experimentsprobing high lying excited states in dense alkali vapor.
I. INTRODUCTION
Vapor cells are attractive compact platforms for fun-damental physics and quantum technology experiments.For most applications, alkali metal vapor cells are re-quired to operate in elevated temperatures to increase theavailable atomic density. Under these conditions the ef-fects of BBR and of inter-atomic collisions on the atomicpopulation distribution and lifetime become of impor-tance, particularly for experiments involving highly ex-cited atomic states that are now more easily accessibledue to advances in laser diode technology.Probing atomic vapors at elevated atomic density re-quires understanding of collisional mechanisms. Collisionassisted velocity redistribution (thermalization) withinthe hyperfine manifold of the cesium 6 P levels [1] hasbeen measured in vapor cells and has been of importancefor experiments near surfaces [2–4]. Collisional effectshave also been studied for higher lying states like the7P [5–7] and the 8P [8, 9] levels of cesium, where in-direct evidence of BBR redistribution was also reported[8]. Nevertheless, the effects of collisions in redistribut-ing or thermalizing the atomic velocities has remainedso far unexplored for high-lying excited states for whichradiation trapping and resonant exchange collisions withground state atoms are expected to reduce. This couldunmask collisional mechanisms that preserve a memoryof the laser selected velocities, previously studied mainlywith molecules [10] or buffer gas perturbers [11–13].The interaction of atoms with BBR has been mainlystudied for Rydberg atoms [14–19], that have manydipole couplings at mid and far infrared (thermal) wave-lengths. The depopulation of Rydberg states due to BBR ∗ [email protected] has been studied experimentally and theoretically in thevolume [18, 19] or inside a cavity [20]. The effects ofBBR have also been studied on trapped molecules forwhich BBR is the main thermalisation mechanism [21].Our group is interested in the interaction of atoms withthermal fields in the near field of a hot surface [3, 4, 22–24]. Contrary to far-field BBR, near field thermal emis-sion is monochromatic due to the thermal excitation ofevanescent surface polariton modes [25, 26]. The near-field redistribution of the atomic excitation is expectedto display distinct characteristics that need to be dis-criminated and distinguished from volume redistributiondue to collisions or BBR. The cesium 7P atoms are ofparticular interest in such experiments due to their cou-pling with the 6D states that coincides with the sapphirepolariton modes [3, 22, 27].Here, we investigate far-field BBR and collision redis-tribution mechanisms, from cesium 7P levels, in the vol-ume of a sapphire cell. The unusual feature of our cellis that its main body can be heated to high tempera-tures up to 1000 K, while the cesium density is almostindependently regulated via the temperature of the ce-sium reservoir. The pump laser, exciting atoms to the7P level, also selects the atomic velocity along the beampropagation axis. At moderate cesium densities we studyvelocity preserving BBR transfer to the 6D states byprobing the 6D →
7F transition (see Fig.1a). Our set-up allows us to explore BBR effects from 400 K up to1000 K. We also study collisional redistribution withinthe fine and hyperfine states of the 7P levels by probingthe 7P →
10S transitions (see Fig.1a). Our experimentsallow measurements of the velocity distribution of the ex-cited state population. We show that radiation trappingand exchange collisions with the ground state do not ef-ficiently thermalize velocities in the 7P levels. Instead,we observe the existence of fine and hyperfine structurechanging collisions that preserve the velocity selection. a r X i v : . [ phy s i c s . a t o m - ph ] J a n These collisions possibly involve two excited atoms whosevelocities are selected by the pump laser.
II. EXPERIMENT AND RESULTS
A schematic of our pump-probe experimental set-upis shown in Fig.1b. Our cell is an 8cm long sapphiretube onto which two sapphire windows are attached us-ing a high temperature mineral glue [4, 28]. The cell waspreviously used to perfom atom-surface interaction mea-surements at high temperatures up to 1000 K [4]. Themaximum operating temperature of the first window isabout 1300 K. The cell contains a sidearm, which actsas a cesium reservoir, glued around a hole drilled on thesecond window. The maximum operating temperature ofthe second window is about 700 K.Two independent ovens control the cell body tempera-ture and a third oven controls the reservoir. Inside eachoven, the temperature is measured by thermocouples thatare in contact with the first window, T cell , second win-dow, T inter , and and cesium reservoir, T r . The experi-mental error bars in these measurements are ∆T ≈
30 K,mostly due to systematic uncertainties. Below 700K thetemperature of the cell body (T inter and T cell ) is kept ashomogeneous as possible within the experimental preci-sion of the temperature measurements. However, for val-ues of T cell larger than 700 K, T inter stays fixed at 700 Kin order to protect the cell. This means that the cell bodytemperature is inhomogeneous. The effective tempera-ture relevant for our measurements is often T cell , depend-ing on the laser beam propagation inside the cell. Thereservoir temperature (T r ) is varied from 330 K to 470 K.Our studies [27] have shown that the cesium vapor pres-sure inside the cell can be considered constant, defined bythe reservoir temperature,P(T r ), while the cesium den-sity depends on the local temperature of the cell body.When the temperature of the body is homogeneous thecesium density is given by n Cs = P(T r ) / k B T cell , wherek B is the Boltzmann constant.A 459 nm or a 455 nm extended cavity laser diodepumps the cesium atoms to the 7P / or 7P / levelrespectively. An auxiliary saturated absorption set-upis also implemented in order to calibrate the frequencyof the lasers. Before entering the cell, the beam passesthrough a pinhole after which it is collimated with a di-ameter of 3-4 mm. This creates a smooth beam profilewithout any intensity spikes. The maximum pump powerentering the cell is ≈ . . µ m. The laser can be scanned continu-ously over several GHz with a very good scan frequencyreprehensibility. The probe beam is also spatially filteredthrough a pinhole and collimated to a diameter of about3 mm (slightly less than the pump beam diameter). FIG. 1. (a) Schematic of the cesium levels relevant forthis experiment. The BBR couplings relevant for this experi-ment can occur in the 7P / → / transition at 12 . µ mand in the 7P / → / and 7P / → / transitions at15 . µ m and 14 . µ m respectively. The 8S, 8P, 4F levels(grey color) are relevant for our numerical calculations. (b)Schematic of the experimental set-up. The two lasers are superposed using a dichroic mir-ror before entering the cell. For the range of cesiumdensities explored here, the blue pump is absorbed inthe body of the cell. For the highest cesium densities(n Cs ≈ . cm − ) the pump beam is almost fully ab-sorbed within ≈ µ m inside the cell. This means thatnear-field effects can be ignored as they are only im-portant in the nanometric regime [27, 29] for distancesless than 1 µ m. Only for very low cesium densities (forn Cs below ≈ . cm − ) the blue pump is not fully ab-sorbed inside the 8cm long cell. For this purpose, at theother end of the cell the beams are separated using an-other dichroic mirror and their power is monitored by asilicon (blue light) or a germanium (infrared light) pho-todiode. Bandpass filters are also used to ensure thatonly light of the appropriate wavelength reaches our de-tectors. In all cases, the absorption of the infrared proberemains small, on the order of 10-100 ppm.The principle of the experiments is the following: astrong blue laser at 459 nm (455 nm) pumps atoms tothe 7P / level (7P / ). The pump laser selects atomswith a narrow class of velocities along the beam prop-agation axis. The velocity selection is much narrowerthan the Doppler width and in most cases is consid-ered negligeable. BBR and inter-atomic collisions redis-tribute the atomic population to neighboring energy lev-els (Fig.2). The probe transmission spectrum, demodu-lated at the AM frequency of the pump, is then measuredas a function of cesium density (n Cs ) and cell temperature(T cell ). The demodulated transmission is the differencebetween the pump-on ( P on ) and pump-off ( P off ) trans-mitted probe powers, divided by P off . Collisional processinvolve at least two atoms having nonlinear dependenceon atomic density. As a general, but not absolute rule,collisions tend to redistribute the excitation in a broaddistribution of atomic velocities [1, 30, 31]. In contrast,BBR radiation does not affect the atomic velocity (herethe recoil kick can be ignored) and is a linear processwith respect to the total number of atoms on the 7P / excited level. BBR redistribution
FIG. 2. (a) Transmission of the infrared probe laser (after de-modulation) tuned at the 6D / → / transition as a func-tion of the laser frequency for various cesium vapor densitiesand for T cell = 490 K. At low cesium densities sub-Dopplerpeaks are observed attributed to a 7P / → / velocitypreserving BBR absorption (see main text). The componentsF (cid:48)(cid:48) = 2 , , α = 0 m / swhereas components F (cid:48)(cid:48) = 3 , , β = −
173 m / s). The scans are centered on theF (cid:48)(cid:48) = 4 (u α = 0 m / s) hyperfine component. For the first set of experiments described here, theinfra-red probe laser is scanned around the 6D → cell = 490 K. Here, the pumplaser is tuned on the 6S / (F = 4) → / (F (cid:48) = 3) tran- sition frequency, with a power of ≈ . pump , k probe respectively. At low densities, the influ-ence of collisions can be ignored. This suggests thatground state atoms with a velocity u α (here u α = 0) arepumped to the F (cid:48) = 3 hyperfine level of 7P / , whereasatoms of velocity u β , with k pump u β = k pump u α − π ∆(here u β = −
173 m / s), are pumped to the F (cid:48) = 4 hy-perfine level of 7P / . Here ∆ = 377 MHz is the fre-quency spacing of the hyperfine manifold, whereas u α and u β are the velocity components along the beampropagation axis. BBR pumps the former velocityclass to the 6D / (F (cid:48)(cid:48) = 2 , ,
4) levels and the latterto 6D / (F (cid:48)(cid:48) = 3 , , / → / tran-sition, leading to the six peaks in Fig.2. Whenthe pump laser is detuned by δ pump with respect tothe 6S / (F = 4) → / (F (cid:48) = 3) frequency then allsix peaks shifts by δ pump k probe k pump (for our experiments k probe k pump ≈ .
3) consistent with velocity selective pumpprobe spectroscopy. The observed linewidth of the peaksis limited to about 5MHz. This value does not dependon density and is similar for all the observed peaks, sug-gesting that it is probably related to the frequency insta-bilities of the lasers at timescales of a few seconds (timerequired to scan the frequency around a peak). The hy-perfine manifold of the 7F / level is not resolved here,suggesting that hyperfine structure frequency spacing iswell below 5MHz. This sets an upper limit for the mag-netic dipole constant, | A / | < . ≈ cm − the ef-fects of collisions are negligible and the transmission spec-trum is independent of cesium density (see light graycurve in Fig.2). This is clear proof that in this regimecollisional mechanisms are not involved in the observed7P / → / transfer. As the atomic density increases,one notices a broadening of the peaks as well as the ap-pearance of a Doppler broadened background that even-tually dominates the spectrum (Fig.2). Both these effectscan be attributed to collisions.In Fig.3 we plot the amplitude of the sub-Dopplerpeaks as a function of cell temperature, while keepingthe vapor density at moderate levels and therefore en-suring that collisional transfer to the 6D / level is neg-ligible. We show the amplitudes of transitions startingfrom 6D / (F (cid:48)(cid:48) = 2 , ,
4) levels (for atoms with velocityu α =0 m/s) as well as transitions from 6D / (F (cid:48)(cid:48) = 3 , , β =-173 m/s). The ampli-tudes are divided (normalized) by the relative weights ofthe 7P / (F (cid:48) ) → / (F (cid:48)(cid:48) ) hyperfine transitions. Theseare (15 / , / , /
56) and (7 / , / , /
72) for theF (cid:48) = 3 → F (cid:48)(cid:48) = 2 , , (cid:48) = 4 → F (cid:48)(cid:48) = 3 , , (cid:48)(cid:48) = 3 , , FIG. 3. Amplitude of all the sub-Doppler peaks observedat the 6D / → / transition, divided (normalized) bythe relative weights of the 7P / (F (cid:48) ) → / (F (cid:48)(cid:48) ) hyperfinetransitions. Filled points correspond to transitions start-ing from F (cid:48)(cid:48) = 2 , , α = 0 m / swhereas open points to F (cid:48)(cid:48) = 3 , , β = −
173 m / s. The error bar associated with the T cell mea-surement is ≈
30 K. The dashed curves represent the ex-pected evolution according to the Bose-Einstein factor. Thereservoir temperature is fixed at T r =370 K. The cesium den-sity varies with T cell approximately from 1 . · cm − to5 . · cm − . tion ratio of the two velocities multiplied by the strengthratio between the 6S / (F = 4) → / (F (cid:48) = 3 ,
4) tran-sitions. For temperatures below 700 K (in this rangethe cell body temperature is homogeneous), the ampli-tude evolution of all peaks follows Bose-Einstein statis-tics given by n( λ, T cell ) = [e hc(kBTcell) λ − − , where h isPlanck’s constant, c the speed of light and λ the wave-length. This demonstrates that the population trans-fer is due to BBR. As aforementioned, when T cell ishigher than 700 K, the temperature of the second win-dow, T inter , stays fixed at 700 K. In this case the temper-ature of the cell body is inhomogeneous. For this reason,the experimental points in Fig. 3 fall below the theoret-ical expectations that do not account for a temperaturegradient of the cell temperature.Furthermore, we have conducted experiments on the6D / → / transitions, shown in Fig. 4. The6D / level cannot be directly populated by BBR as the7P / → / transition is dipole forbidden. At high va-por densities collisional mechanisms distribute the excita-tion from the 7P / to the 6D / level. A broad spectrumis observed suggesting that the excitation is distributedto a wide range of velocities. It should be noted thatpump power and frequency were the same for the experi-ments of Fig.2 and Fig.4. The two figures are plotted onthe same vertical scale for a direct comparison betweentransfer mechanisms.Experiments were also performed using a 455 nm laser FIG. 4. Probe transmission (after demodulation) at the6D / → / transition for various cesium densities atT cell =800 K. The scans are centered on the peak of the spec-trum. The FWHM spread of the distribution is ≈ Cs = 1 . · cm − and ≈ Cs = 8 . · cm − .The hyperfine structure spread of the 6D / is ≈ pumping the atoms to the 7P / level and a probe laserscanning around the 6D →
7F transitions. In this case,the signals are also sub-Doppler but significantly morecomplicated due to the hyperfine manifold of the 7P / levels. Discussion
Our studies of BBR excitation redistribution focus pri-marily on the 7 P → D channel. In principle BBR cantransfer the initial excitation to many adjacent energylevels with transfer rate proportional to the Bose-Einsteinfactor at a given transition wavelength. To estimate thepopulation of energy levels surrounding the 7 P pumpinglevel we have solved the system of rate equations (see[8] for more details) in the low density and low powerlimit when collisions and saturation can be safely ignored.Our calculations show that the excitation is mainly dis-tributed to the 6D, 8S and 7D levels (see Fig.1a) by BBRtransfer and to lower lying states , such as the 7S and 5D,by both spontaneous emission and BBR transfer (bothpreserving the atomic velocities [35]). Interestingly, ourcalculations show that for high temperatures the 8P and4F levels can also be significantly populated due to two-step BBR excitations. For example, at T cell =1000 K,8P and 4F populations are about 6 .
5% and 1 .
3% of the6D / population (probed in our experiments) whereasthe 8S population is about 80% of the 6D / popula-tion. This suggests that using a similar set-up, one coulduse the 4F → nG transitions to perform high-resolution,sub-Doppler spectroscopy of nG / and nG / levels thatare normally accessible via quadrupole-quadrupole spec-troscopy from the ground state [36]. Similarly, spec-troscopy of higher nP levels can be performed on the8S → nP transitions that also lie in infrared wavelengths.However, for these experiments the available signal willbe significantly reduced. Collisional redistribution
While the collisional redistribution within the 6 P levelhas been experimentally studied in the past [1, 3, 22],similar studies for high-lying states have been scarce. Inorder to study collisional redistribution processes withinthe 7P manifold we turn our infrared laser on resonancewith the 7P / → / transition at 1530 nm. In theseexperiments the beam waist of the lasers (pump andprobe) was reduced ( ≈ µ m) in order to increase theavailable pump intensity. This allows us to achieve inten-sities significantly higher than the saturation intensitiesof the 7P levels ( ≈ mW / cm and ≈ mW / cm forthe 7P / and the 7P / respectively [37]). In the first ex-periment, we probe the 7P / → / transitions whilepumping directly the atoms to the 7P / level. Thisallows us to study the redistribution of the excitationwithin the hyperfine manifold of the 7P / level.In Fig.5a we plot the infrared probe transmissionthrough the cell for three different cesium densities andfor a cell temperature of T cell = 570K. The 459 nmlaser pumps atoms of u α = 0m / s and u β = − / s tothe F (cid:48) = 3 and F (cid:48) = 4 hyperfine levels of 7P / respec-tively. These atoms are probed by the infrared laser,leading to the four main peaks of the infrared trans-mission spectrum (Fig.5). F (cid:48) = 3 → F (cid:48)(cid:48) = 3 , α atoms) at 0 MHz and -252 MHz and F (cid:48) = 4 → F (cid:48)(cid:48) = 3 , β atoms) at -742 MHz and -490 MHz. At verylow cesium densities (light gray curve) these are theonly observed peaks. Strikingly, additional sub-Dopplerpeaks appear as cesium density increases. These peaksseem to correspond to a collisional transfer of u β and u α atoms to the F (cid:48) = 3 and F (cid:48) = 4 levels respectively. Thisshould lead to four additional peaks: F (cid:48) = 3 → F (cid:48)(cid:48) = 3 , β atoms at −
113 MHz and −
365 MHz (shifted by − ∆ k pump k probe ≈ −
113 MHz with respect to those observed foru α atoms) and F (cid:48) = 4 → F (cid:48)(cid:48) = 3 ,
4, for u α atoms at -629MHz and -377 MHz (shifted by ≈ +113 MHz with respectto those observed for u β atoms). The above hypothesisis consistent with the observations as the -377 MHz and-365 MHz peaks partly overlap. Although a broad col-lisional background also appears, the sub-Doppler peaksremain visible for very high densities. It is worth not-ing that the width of the additional peaks is similar tothe that of the main peaks (corresponding to the atomsdirectly pumped by the 459 nm laser).Fig5a shows that the additional sub-Doppler peaks de-pend on cesium density. This demonstrates that thepeaks are due to a collisional transfer and not due to two step BBR processes that could in principle redis-tribute the excitation within the hyperfine levels whilepreserving the atomic velocities. Furthermore, we haveused the previously mentioned rate equation model tocalculate the population redistribution between the hy-perfine components of 7P / due to two-step BBR pro-cesses. According to our findings, for a cell temperatureof T cell =570K two-step BBR processes are negligible andcannot account for the findings of Fig5. FIG. 5. Probe transmission (after demodulation) of the in-frared probe laser tuned at the 7P / (F (cid:48) ) → / (F (cid:48)(cid:48) ) tran-sition. (a) Transmission spectrum for different cesium densi-ties. The 459 nm pump laser power is 200 µ W and the celltemperature is T cell =570 K. The four main (directly pumped)peaks are denoted on the graph F (cid:48) = 3 → F (cid:48)(cid:48) = 3 , α (black letters) and F (cid:48) = 4 → F (cid:48)(cid:48) = 3 , β (gray letters). Additional sub-Dopplerpeaks appear when cesium density increases (b) Transmissionspectrum for different pump powers with n Cs =8.3 10 cm − and T cell =570 K. The inset shows the amplitude of the ad-ditional peak (indicated on the graph) as a function of theamplitude of the direct peak (indicated on the graph) for dif-ferent pump powers (150 µ W, 300 µ W, 700 µ W and 1300 µ W).
In Fig5b we show the the 7P / → / transmis-sion spectrum for two different pump powers (150 µ Wand 1300 µ W). We can observe that the amplitude evolu-tion of the direct peaks increases sub-linearly with pumppower verifying that the pump laser saturates the 459nm transition. More importantly, we observe that theadditional sub-Doppler peaks increase much faster withpump power compared to the main peaks while the widthof direct and additional peaks remains comparable. Theamplitude of one additional peak is plotted as a func-tion of the amplitude of one direct peak for four differentpump powers (150 µ W, 300 µ W, 700 µ W and 1300 µ W)in the inset of Fig.5b. The points follow a super-lineartrend. The above observations are a strong indicationthat the collisional mechanism, giving rise to the addi-tional sub-Doppler peaks, involves collisions between twoexcited atoms. Such collisional mechanisms should de-pend quadraticaly on the excited state population (seeDiscussion section below). Here, the amplitude of thedirect peaks depends on the excited state population di-rectly pumped to the 7P level, while the amplitude of theadditional peaks depends on the collisionally transferredpopulation. This justifies the super-linear dependence ofthe additional peak amplitude as a function of the directpeak amplitude, shown in inset of Fig5b.Surprisingly, the additional sub-Doppler peaks corre-spond to a collisional but velocity preserving transfer be-tween the hyperfine manifold of the 7P / level. Addi-tionally, our experimental findings strongly suggest thatthis collisional mechanism involves two velocity selectedexcited atoms. This observation is in direct opposition tothe collisional redistribution measured within the 6P / hyperfine manifold that shows little or no evidence ofvelocity preservation [1].In the second experiment we pump the atoms to the7P / level while still probing the population of the 7P / level. In Fig. 6 we show the probe transmission spec-trum at the 7P / → / transition for two differentpump laser powers. Here T cell =490 K and n Cs =8.3 10 cm − . The 7P / level is populated by collisions thatredistribute atoms within the 7P fine structure. As inthe previous case the transmission spectrum clearly dis-plays evidence of velocity selection. The peaks observedin the spectrum are here roughly 70 MHz broad but sig-nificantly narrower than the Doppler FWHM linewidthof ≈
270 MHz. It should be noted that pump laserselects three velocities, one for each hyperfine transi-tion F = 4 → F (cid:48) = 3 , ,
5. Here, the hyperfine spacingF (cid:48) = 3 , , k probe k pump giving ≈ FIG. 6. Probe transmission (after demodulation) on the7P / → / transition at 1530 nm when the pump istuned on the 6S / (F = 4) → / (F (cid:48) = 5) transition. HereT cell =490 K and n Cs =6.8 10 cm − . The 7P / level ismainly populated by collisions. The scans are arbitrarily cen-tered on the peak of smallest frequency. The Doppler FWHMwidth is shown for comparison. The transmission spectrumis measured for two different pump powers 1 mW (black line)and 0.2 mW (gray line). The gray curve is multiplied by afactor of 10. The lineshapes of the two curves are not thesame indicating an interplay between linear and super linearprocesses. tion to the 7P / level. This mechanism would lead toa quadratic dependence of the transmission signal with7P / population (that is defined by pump power). Nev-ertheless, in the conditions of our experiment it is diffi-cult to predict the exact dependence of the transmissionspectrum as a function of pump power because: (a) colli-sional transfer to the Cs(7P / ) can also be achieved viacollisional processes between Cs(7P) and Cs(6S) atoms[5, 38], which should lead to a broad background vary-ing linearly with 7P / population (b) saturation of thepump transition leading to a sub-linear dependence ofthe transmission spectrum with pump power cannot beignored as the saturation intensity of the pump transitionis ≈
15 mW/cm . Discussion
We now discuss the underlying collisional mechanismsthat could explain our experimental observations. Ex-change collisions between 7P and 6S are expected to re-distribute the atomic population and atomic velocitieswithin the fine and hyperfine manifold of the 7P state.The kernel of exchange collisions [30, 39] is broad with asmall memory of the initial velocity leading to fast ther-malization. The number of such collisions per unit timeand unit volume is proportional to ∼ k G · n G · n E , wherek G is the collision rate coefficient of the process, n G is theground state population (approximately equal the totalcesium density) and n E is the excited state (7P) popu-lation. This process is therefore sub-linear with pumppower (linear in the weak pumping regime). These colli-sional mechanisms could explain the Doppler broadenedbackground observed in Fig.5 and Fig.6 but are unableto explain the behavior of the observed sub-Doppler con-tributions.Instead the sub-Doppler contributions seem to origi-nate from collisions between excited state atoms with ve-locity components u α and u β , selected by the blue pumplaser. Velocity selection is also preserved after sponta-neous emission to the downward 6D and 7S levels (seeFig.1a) [35] but is probably lost after further decay tothe 6P level [1]. For collisional processes between ex-cited state atoms the number of collisions per unit timeper unit volume is proportional to ∼ k E · n · n , with k E the collision rate coefficient and n , n E the populationof the two excited states involved in the collision. Theseprocesses can be super-linear with pump power and areconsistent with the observations of Fig. 5 and Fig. 6.One possible mechanism that can lead to hyperfinestructure redistribution is resonant exchange collisionsbetween two velocity selected atoms of 7P and 5D or 7Slevels, both significantly populated due to spontaneousemission (n ≈ . while n ≈ . ). This wouldbe according to the process:Cs(7P / , F , u α ) + Cs(5D / , F (cid:48) , u β ) → Cs(7P / , F , u β ) + Cs(5D / , F (cid:48) , u α ) (1)The above process does not require deflection of veloci-ties and therefore the selected velocity components (alongthe pump propagation axis) u α and u β can be preserved[1]. The collision rate per unit volume of such resonantexchange collisions should depend quadraticaly on the ex-cited (7P population), assuming that spontaneous emis-sion stays the dominant population mechanism of the 5Dor 7S levels.Finally, we note that fine structure redistribution couldbe possibly due to a different process as it also involves asignificant change of the internal energy of the products.Our experiments show that fine structure redistributionis less efficient (the signal amplitude of Fig.6 is smallerthan that of Fig.5 for similar pumping strength) causingadditionally significant broadening of the initial velocityselection. III. CONCLUSIONS
Our experiments study the redistribution of an atomicpopulation, initially pumped to the second cesium reso-nance, to many adjacent energy levels. At high cesium densities, this redistribution is mainly due to collisions.We show that collisional redistribution within the 7P lev-els can happen via fine structure changing and hyper-fine structure changing collisions between excited stateatoms that preserve the atomic velocities. We observealso that exchange collisions and radiation trapping arenot effective in redistributing (thermalizing) the excita-tion in the 7P state. This is in sharp contrast with ob-servations performed for the cesium 6P state, where theinitial velocity selection of the pump is almost lost even atvery low densities [1]. State changing collisions preserv-ing atomic velocities could become even more prominentfor higher lying excited atomic states and Rydberg atoms[40] where the importance of resonant exchange collisionswith ground state atoms is expected to diminish. In thisrespect, the collisional mechanisms observed here couldplay a role in measurements of collective effects betweenRydberg atoms in thermal vapor cells [41, 42] as well asin measurements of Rydberg population [43] or buffer gasdensity [44] using Rydberg ionization via collisions or to alesser extent by BBR [45]. Additionally, our observationscan be of importance for two-step Rydberg spectroscopyvia the second instead of the first atomic resonance.At low cesium densities we observe velocity preserv-ing redistribution of the initial laser excitation due toabsorption of BBR photons. Our experiments are per-formed in the volume of the cell where broadband BBR(Planck spectrum) significantly populates a plethora ofenergy levels at high temperatures. This velocity pre-serving process can provide a simple way of performinghigh-resolution spectroscopy of highly excited energy lev-els of alkali atoms. We also discuss the possibility of ex-ploiting two step BBR processes to perform sub-Dopplerspectroscopy of cesium nG / and nG / states. Finally,we mention that BBR transfer can be also important inthe study of low lying states such as 6P cesium, in par-ticular on the 6P →
5D or 6P →
7S channels.An interesting perspective whould be to study thenear-field 7P / → / transfer due to thermally ex-cited sapphire polaritons [3, 27]. This can be achieved byprobing the 6D / → / transition near the sapphiresurface using selective reflection spectroscopy [29]. Thesignature of this near field energy transfer mechanismneeds to be discriminated from collisional or far-fieldBBR transfer, studied in this paper, that affect atomsin the volume of the cell. ACKNOWLEDGMENTS
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