Cooling All External Degrees of Freedom of Optically Trapped

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Vernac, L. Gorceix, O. Lepoutre, S. Gabardos, L. )[]adebu ( erbium and [3] 8) = d − P.S.D. aelk insta- wave-like sn ryMolasses Gray Using Dtd eebr2,2018) 24, December (Dated: of 39 J S ≈ and K 1 6) = 3) = . 7 − 3 hs xeiet r efre ihna optical an within performed are experiments These . 41 hills. potential hoim h anrao sta ae-oln with laser-cooling that the is in reason molasses in gray main difficulties The laser-cooling the chromium. circumvent to means lent experiments recent more line. any of this aware along not are we but [24] neo ieetknso ih oaiainadinten- with atoms and that pres- insures polarization VSCPT light the The of to [25]. gradients kinds due sity different cooling of Sisyphus trap- ence and population coherent (VSCPT) selective ping velocity of bination [21], o Dcoigo hoimtemlba sn gray using beam the thermal in chromium molasses a of 1D-cooling for rniin u oaoi oin(hr oi ros from arrows) solid (short motion atomic | to due Transitions yatikrapc fteproi oeta.Tee atoms There, potential. toward illustra periodic pumped as the optically hills of rapidly potential aspect are the thicker of a part by upper the in entially a oeta.Tastosdet h ae ih ln sol (long light laser the to due between Transitions arrows) potential. flat a ope state coupled n Mlsrbaslast iuodlproi CStark AC periodic state sinusoidal coupled a the differ- to for the potential leads between shift beams Interference taking laser stage. VSCPT GM and GM ent cooling the Sisyphus during the place of Principle 1. FIG. ψ 1]adte to then and [17] K NC efidta h rymlse prahi nexcel- an is approach molasses gray the that find We i 87 to b[2 n metastable and [22] Rb tteqatmregime. quantum the at g l xhnetesailadvelocity and spatial the exchange lly se ussco l xenldegrees external all cool pulses asses | etevlct itiuin n free and distribution, velocity the ze ψ esae h bandsmlsare samples obtained The space. ee iy( sity C i | ψ cu rfrnilyi h oe ato the of part lower the in preferentially occur hsqedsLasers, des Physique e NC | P.S.D. ψ lin C i 3 iltnue France Villetaneuse, 430 hymagnetic ghly i osntsetelgtadteeoehas therefore and light the see not does ⊥ n h xie state excited the and σ yafco of factor a by ) + 40 lin [18], K − hoimAtoms Chromium d ofiuainwsrpre in reported was configuration σ Tolra − ofiuainue com- a uses configuration 4 52 7 e[3.Frtevidence First [23]. He | i[19], Li ψ ratoms. Cr | ψ C NC i ≈ oee,tenon- the However, . i 250, | ψ dse arrows). (dashed 6 e i[20], Li i cu prefer- occur 23 ted Na id 2

FIG. 3. Evolution of the phase-space density when atoms are loaded in the optical dipole trap, when a single gray molasses FIG. 2. Relevant energy levels and transitions used for the pulse is performed (GM) and when the scheme to cool all ex- magneto-optical trap, the optical dipole trap (ODT) and gray ternal degrees of freedom with multiple GM pulses is applied. molasses.

the trap therefore results in a π/2 rotation in phase- small velocities remain in states not coupled to the light space when the evolution time is a quarter of the trap (the ”dark states”) built by the dressing induced by the period T/4 (thus exchanging spatial and velocity degrees gray molasses (GM) laser beams for any J → J or of freedom). Two molasses pulses performed in the opti- J → J − 1 transition. Moving atoms in the coupled cal dipole trap (ODT) separated by a T/4-long free evo- states lose kinetic energy through Sisyphus cooling while lution can therefore cool both the spatial and velocity moving atoms in the non-coupled states can return to distributions. This technique was first applied in [29, 30] the coupled state thanks to motional couplings (Fig. 1); (although not in the context of gray molasses) and the these non-adiabatic transitions occur with a v2 depen- phase-space manipulation is also reminiscent of the delta- dence [26] such that the coldest atoms are stored in dark kick cooling technique [31, 32]. The combination of cool- states where they are protected from light-assisted col- ing and compression techniques applied along the three lisions. The Sisyphus cooling mechanism benefits from space axes insures that all external degrees of freedom the high friction force even more so because chromium are cooled. We reach a temperature below 10 µK in the involves blue (λ = 429 nm) cooling light and the friction optical trap. The overall increase in the phase space den- coefficient scales as 1/λ2 [27]. sity brought by this procedure is between two and three Furthermore, the absence of hyperfine structure in the orders of magnitude, leading to a trapped sample with 5 presently studied case of bosonic Cr results in a simple ≈ 4.10 Cr atoms at a very favorable phase-space den- −3 scheme with no need for repumpers. Our laser beam sity of (1.7 ± 0.9) × 10 (Fig. 3). arrangement for implementing the gray molasses therefore involves only three retro-reflected laser beams in the σ+ − σ− configuration along three orthogonal directions GRAY MOLASSES, MAIN MECHANISMS of space, with the laser frequency blue-detuned with re- 7 7 spect to the S3 → P2 transition at 429 nm (Fig. 2). We now introduce the main physical mechanisms in- We find that our gray molasses cooling scheme brings volved in gray molasses. First, the use of a J → J − 1 all atoms from a pre-cooled temperature of 60 µK to transition insures that there exists at least one dark state, 8 µK in 3.5 ms, thus insuring that light-assisted losses formed by a superposition of different Zeeman states in are negligible [13, 14]. The temperature which is reached the electronic ground state. The general form of those dark states can be written ψ = P αDS |m i. The T ≈ 4 Trec (where Trec ≈ 2 µK is the recoil temperature), DS mS mS S is close to the ultimate limit for gray molasses beyond DS actual linear superposition αmS depends on the Rabi fre- which the capture velocity gets below the r.m.s. velocity quencies, the detunings, and the phases of the different of the atoms in the thermal cloud [27]. DS laser beams. For this reason, the coefficients αmS indi- Additionally, we find that Cr gray molasses work rectly depend on the velocity v of the atoms. In other so equally well in free space as within an optical dipole trap called bright dressed states, absorption of light is possible as already reported for cesium [28] and lithium atoms then followed rapidly by spontaneous emission. [20]. This allows us to perform successive pulses of gray When atoms are in the bright states, they experi- molasses inside the trap, separated by a free evolution ence a position dependent periodic AC Stark shift asso- time of the atomic cloud. For our parameters, the trap- ciated with the molasses beams. This periodic light-shift ping potential is nearly harmonic. A free evolution in arises from the polarization gradients created by the laser 3

7 7 FIG. 4. Evolution of the temperature (left) and the atom number (right) with respect to the detuning from the S3 P2 transition with the optical dipolar trap turned on (red dots) or off (blue triangles). In all the graphs in this paper, the→ error 1 N 2 bars indicate σ with σ = (xi x) the standard deviation obtained from N data points (typically N 5). ± q N Pi=1 − ≈ beams. Atoms also experience a corresponding spatial dependence in the dissipative part of their interaction with light. Crucially, blue detuning the laser frequency compared to resonance insures that dissipation is highest when the potential of the AC Stark shift is maximum. This results in a Sisyphus mechanism such that optical pumping is mostly happening where potential energy is maximum [27]. Blue detuned molasses in a J → J − 1 configuration are particularly efficient because optical pumping pop- ulates dark states. If the velocity of atoms is close to zero, atoms can remain in these dark states for very long times, in a VSCPT scenario. If however atoms possess a FIG. 5. Evolution of the temperature (blue dots) and atom finite velocity, their motion through the polarization gra- number (green triangles) with respect to the magnetic field in one direction of the horizontal plane in the absence of the dients results in a dynamical change of the dark dressed ODT. The molasses phase duration is 3.5 ms, the intensity is i.e. DS states ( of the αmS ). This leads to a non-adiabatic ramped down after the initial 0.5 ms as described in the text coupling from the dark states to the bright states with a and the detuning is set at δ = 9.4 Γ. A similar behavior is rate scaling as v2 and occurring preferentially when the observed in the other two directions of space. energies of the dark and bright states are closest due to non-adiabatic following [26]. Once the atoms are back in the bright states, they can again undergo Sisyphus cooling before being pumped again in a dark state with, in average, a lower velocity. We now introduce the main physical quantities at play to evaluate the efficiency and the limits of gray mo- captured in gray molasses, it is especially important for 7 7 lasses (with Γ the linewidth of the S3 → P2 transi- their velocity to be below vc, since the light is blue de- tion, λ the laser wavelength, Ω the associated Rabi fre- tuned, and the traditional Doppler mechanism thus gen- quency and δ the detuning). The scattering rate in bright erates heating. Below vc however, the friction force of the states or equivalently the optical pumping rate is given Sisyphus cooling overcomes this heating process. The ul- by Γ′ ∝ Ω2/4δ2 ×Γ (with δ > Γ). The capture velocity is timate limit of cooling is reached when the capture veloc- ′ vc =Γ /k: only atoms with v ≤ vc will be cooled down. ity vc approaches the velocity associated with the r.m.s. 2 2 The molasses temperature is kBT ∝ ~Ω /δ, provided the temperature of the cloud ~Ω /δ. This sets a minimum associated r.m.s. velocity is larger than vc. As can be laser power (or maximum δ). Keeping in mind that it is deduced from these equations, the lowest-limit tempera- required for molasses to be efficient that δ > Γ, the low- ture of atoms cooled within gray molasses is set by the est achievable temperature in gray molasses is such that ∗ AC Stark shift in the bright state. On the other hand, the kBT is of the order of five to ten ER as has been verified capture velocity is controlled by the spontaneous emis- in numerous previous experiments with alkali atoms (see sion rate in the bright state. For atoms to be efficiently attached Table I). 4

EXPERIMENTAL SETUP

Our experimental setup has been described in [33]. We first run a standard magneto-optical trap, with λ = 425 7 nm laser beams, red detuned compared to the S3 → 7 P4 electronic transition. We superimpose on this trap a one-beam optical dipole trap provided by a far red- detuned λODT = 1075 nm laser beam propagating along a horizontal direction. To optimize loading of the trap, FIG. 6. Scheme to cool all degrees of freedom in the ODT. we apply a depumping laser beam at 427 nm, close to The first molasses pulse reduces the width of the momentum the 7S → 7P electronic transition. The combination distribution of the atoms. These are then left to evolve in 3 3 the ODT for a quarter of the trap period, leading to a π/2 of this light and the MOT light optically pumps atoms 5 5 5 5 rotation in phase space. Then the second molasses pulse is towards metastable dark states S2, D4, D3 and D2. performed. In each panel, the initial phase-space distribution These states are insensitive to the laser-cooling light, but (p,x) is represented by a shaded area with a dashed outline they are sensitive to the AC Stark shift associated with and the final one by an area with a solid outline. The ar- the 1075 nm light. Optimum loading is realized when the rows represent the effect of the GM pulses on the momentum depumping rate, mostly controlled by the 427 nm laser distribution. intensity, is fast compared to the light-assisted collision rate, and slow compared to the MOT equilibration time. light, is controlled close to the 7S → 7P transition using After typically 200 ms of accumulation in the metastable 3 2 acousto-optic modulators. states in presence of radio-frequency sweeps such that atoms in metastable states do not experience a magnetic field gradient [34], we turn the MOT beams and MOT GRAY MOLASSES OPTIMIZATION magnetic-field gradient off, and repump all atoms from 5 5 5 S2, D4 and D3 into the electronic ground state using three laser diodes running at 633, 654 and 663 nm. First we vary the detuning δ of the gray molasses laser compared to the 7S → 7P transition. The intensity is 5 3 2 This sequence ends up with typically 4.10 atoms in kept at the maximum value of 43 I and the molasses 7 sat the electronic ground state S3, loaded in the optical duration is 0.5 ms. We do not see any decrease in the trap at a temperature of ≈ 60 µK. This temperature, final temperature for longer times. We perform this ex- experimentally found to be ≈ 1/3 of the trap depth [35], periment both within the ODT, and just after the ODT arises from a compromise between the Doppler tempera- is turned off (Fig. 4). The temperature is obtained by ture and evaporation/spilling of the hottest atoms from measuring the size of the atomic cloud in the vertical the ODT. This sample is the starting point for our gray direction following a time-of-flight expansion after being molasses experiment. Note that for this work we used released from the molasses (and the ODT when present). smaller atom numbers than in our typical experiments, We find very similar efficiencies of the gray molasses in ei- simply to increase the oven lifetime. ther case. The optimum detuning is slightly shifted from Gray molasses are produced using light derived from a δ = 2π × 47.3 MHz = 9.4Γ (with Γ = 2π × 5.029 MHz) Ti:Sa laser running at 858 nm, and frequency doubled in to δ = 2π × 42.7 MHz = 8.5Γ when the trap is turned a resonant bow-tie Fabry-Pérot cavity including a LBO on, which is attributed to the fact that the ground and crystal. After injection of an optical fiber, up to 250 excited states do not undergo the same AC Stark shift mWatt are available for laser cooling. The beam is then at 1075 nm. Such a differential light shift is confirmed split into one retro-reflected vertical beam and one retro- by numerical estimates [35], and by the observation that, reflected horizontal beam in a butterfly shape providing during the MOT stage, atoms in the ODT region undergo the four horizontal molasses beams (same configuration stronger fluorescence than away from the ODT, despite 7 as the MOT beams described in [14]). We then have a the fact that only a negligible fraction of S3 atoms are maximum total intensity of 2150 ± 150 mW.cm−2 on the trapped in the ODT. atoms which corresponds to a mean intensity per beam Because the capture velocity vc is small, it is neces- −2 Imax = 358 ± 25 mWatt.cm = 43 ± 3 Isat (where sary to use large laser intensities to capture all atoms −2 Isat = 8.32 mWatt.cm is the saturation intensity of precooled in the MOT. However, once the atoms are cap- the molasses transition). The uncertainty on the inten- tured and cooled, since the molasses temperature is set sity is dominated by the uncertainty on the laser waists by ∝ Ω2/δ, it is favorable to ramp down Ω or ramp up δ at the atoms location. The laser frequency is stabilized in order to further reduce the temperature of the atoms using an ultra-stable Fabry-Pérot cavity, and the abso- until the ultimate limit of cooling T ∗ is reached. Ramp- lute frequency of the laser, determined by monitoring ing down the intensity during the 0.5 ms molasses pulse the fluorescence of the MOT in presence of the 429 nm does not lead to a decrease of the molasses temperature. 5

FIG. 8. Evolution of the atomic cloud size (half-width at 1/e) in the vertical z direction (after a time-of-ﬂight) following FIG. 7. Time sequence for the simplest implementation of a molasses pulse of 0.5 ms (red dots) or two (resp. three) gray molasses and spatial compression, with two gray mo- molasses pulses separated by a quarter of the trap period lasses pulses separated by a quarter-period of the optical dipo- Tz 0.13 ms (orange triangles resp. yellow squares) and a 4 ≈ lar trap in one direction. The 200 ms are necessary to repump wait time of duration t in the ODT. The second and third the atoms from the metastable states. They also allow for the molasses pulses are indicated by the downward arrows. magnetic ﬁeld (MF) to stabilize to its GM value. IGM repre- sents the GM laser beams mean intensity.

For longer molasses durations however, we found it was beneficial to ramp down the intensity after the initial 0.5 ms. For a total duration of 3.5 ms and a ramp down of a few Isat, the temperature decreased from 12.2 to 11.5 µK. For efficient Sisyphus cooling, it is also important to lower the magnetic field amplitudes in all three directions of space. Since atoms are trapped in an optical dipole trap in our experiment, the dynamical control of the fields can be performed without losing atoms and without the reduction in density which inevitably hap- FIG. 9. Temperature (blue dots) and atom number (green pens when the magnetic field gradient of the MOT is triangles) obtained when ramping down the molasses intensity from 36 Isat to I . (The first two pulses were also ramped turned off while the atomic cloud expands in free fall. final down from 43 to 41 Isat and from 41 to 38 Isat in 0.5 ms Away from the null magnetic field, we find that the tem- each.) perature after the gray molasses pulse increases with B, with a sensitivity of ≈ 0.14 µK.mGauss−1. When the magnetic field components are compensated in all three for Cr are as efficient for trapped atoms as for untrapped directions to less than ≈ 3 mGauss, we find an optimum atoms. The principle is described in Fig. 6 and the ex- temperature of 7.7 ± 0.1 µK (see Fig. 5) with a phase- perimental sequence is given in Fig. 7. A first 0.5 ms gray −4 space density of (1.4 ± 0.7) × 10 . molasses pulse is used to strongly lower the kinetic energy of the atoms within the trap. This results in an out- of-equilibrium situation where the energy is not equally COOLING ALL DEGREES OF FREEDOM IN A distributed between the kinetic and potential contribu- TRAP tions. We then use the property that free evolution during a quarter of the trap period T/4 within a harmonic Gray molasses cooling results in almost freezing the trap leads to an exchange between position and momen- motion of the atoms, but provides no spatial compres- tum. At T/4, atoms initially distributed in the cloud sion. Typically, experiments therefore first perform gray volume are concentrated at the bottom of the trap and molasses, before loading the atoms into a conservative their initial potential energy has been converted into ki- trap which is mode-matched to the profile of the atomic netic energy. The final spatial dispersion is set by the cloud. We follow an alternative approach inspired by initial velocity dispersion of the cloud, whereas the ve- [29] combining gray molasses and spatial compression. locity dispersion is raised back to the value it had before We apply the gray molasses cooling to optically trapped the gray molasses pulse. A second gray molasses pulse is atomic clouds, benefiting from the fact that gray molasses then used to lower again the kinetic energy with negligi- 6

To reduce the temperature further we then ramp down the intensity during the third pulse. This time we keep the slope of the ramp constant to −3.9 Isat ms−1 and vary the duration of the pulse. An optimum is obtained for a 2.3 ms pulse and a final intensity of 29 Isat leading to a final temperature of 8.1 ± 0.1 µK (see Fig. 9). We then perform two more molasses pulses to have the same cooling and compression in the two horizontal directions of space y (Fig. 10) and x (Fig. 11). We find that the very elongated direction strongly decouples from the two other directions. In practice, when the two directions with the highest and lowest trapping frequencies (z and FIG. 10. Evolution of the atomic cloud size in the y horizon- y) are cooled in space and momentum, so is the third one tal directions (after a time-of-flight) following three molasses (x). pulses of 0.5 ms separated by 0.13 ms (a quarter of the trap Taken together, four pulses are then sufficient to cool period in the vertical direction) and a wait time of duration t in the ODT. We obtain a trap period in this direction of and compress the whole sample. A reduction of the tem- Ty perature from 60 to 8 µK affecting only the kinetic energy 4 16 ms. At this point, the size of the cloud is minimum and≈ the velocity dispersion is maximum. Another GM pulse would result in an increase of a factor η1 = 20 in phase- is then applied. space density. Our improved scheme where gray molasses pulses are interspersed with free evolution in the trap in- stead leads to a much larger gain in phase-space density, of η2 = 250 (see Fig. 3). In a perfect trap, one expects 2 2 to reach η2 = η1. The discrepancy between η2 and η1 is attributed to anharmonicity. In practice, after a sequence of total duration 20 ms, we end up with a thermal sample consisting of ≈ 4.105 atoms at a temperature of ≈ 8.1 µK at a high phase-space density of ≈ (1.7±0.9)×10−3 in an optical-dipole trap of frequencies about 1.3 kHz and 1.9 kHz along the strongly confining axes and 14 Hz along the weakly confining axis. The characteristic collision times at the beginning and −1 at the end of the cooling sequence are (nσv)initial ≈ 94 −1 FIG. 11. Evolution of the atomic cloud size in the x horizontal ms and (nσv)final ≈ 21 ms, we therefore think that col- direction (after a time-of-flight) following four molasses pulses lisions can be neglected for the 20 ms of the cooling se- of 0.5 ms separated by 16 ms (a quarter of the trap period in quence. We can compare our results to those obtained the y horizontal direction) for the first two and by 0.13 ms (a in [36] with demagnetization cooling of chromium in an quarter of the trap period in the z direction) for the last three optical dipole trap, where a temperature of 6 µK and a and a wait time of duration t in the ODT. The trap period in phase space density of ≈ 0.02 were reached, albeit at the this direction is Tx 0.2 ms. 4 ≈ cost of atom losses due to much longer cooling times of the order of 10 s. ble modification of the atoms spatial distribution. This results in a cloud which is both cooled and compressed, CONCLUSION i.e. a cooling in both position and momentum. We do find that the first gray molasses pulse is followed by a (breathing) oscillation of the radius of the atomic cloud We have combined gray molasses cooling and rotation in the vertical z direction (after release from the ODT, in phase-space to produce ultracold chromium atomic where the atoms were kept for a duration t after the mo- thermal ensembles of high phase-space density. Such en- lasses pulse, and time-of-flight) which is greatly reduced sembles stand as very favorable starting points for fur- after a second molasses pulse at T/4. The breathing mo- ther cooling down to the quantum regime using for ex- tion is still not perfectly frozen however, presumably due ample forced evaporation in a crossed beam optical trap. to the anharmonicity of the trap. We thus apply a third Furthermore the presented scheme could be of benefit pulse and indeed find that the amplitude of the oscillation for other atomic species when gray molasses are possible is reduced further (Fig. 8). At the end of this sequence, within an ODT. the velocity and spatial distributions are cooled along the z direction of space. 7

We acknowledge financial support from Conseil Recherche within CPER Contract, UniversitéSorbonne Régional d’Ile-de-France under DIM Nano-K/IFRAF, Paris Cité, and the Indo-French Centre for the Promotion CNRS, Ministère de l’Enseignement Supérieur et de la of Advanced Research under LORIC5404-1 and PPKC contracts. 8 3 * 5 6 4 5 4 4 5 4 6 − 5 4 − − − − − − − − − 4 5 − − 10 − − 10 10 10 10 10 10 10 10 10 10 10 ø × 10 10 × × × × × × × × × 7 × × . 2 P.S.D. 7 5 1 4 1 8 4 0 ∼ ∼ ...... 2 2 1 1 1 5 1 7 1 4 > or 1 5 6 4 3 0 rec 2 0 7 2 9 7 9 9 ...... 4 T 7 7 5 6 9 3 4 3 14 13 25 53 11 / T 5 5 1 2 . . 4 . . 35 . 1 2 (15 ms) 0 0 3 ∼ 5 7 sat 45 . . 7 ø I . ց ց 14 20 (0.5 ms) 3 2 ց ց within the trap is also given. ց 6 / & 5 6 ց 1 5 I . . 3 . . 17 6 (ramped) d here are those achieving the lowest ∼ 3 43 12 14 ց 13 3 ∼ . 8 l Steck’s website [44]. Recoil temperatures . The parameters given for our paper are for T Γ 5 3 5 3 4 5 8 B ...... 4 5 ø 4 12 10 / 3 2 4 5 5 4 3 (15 ms) δ (0.5 ms) 5 πmk 12 2 . The phase space densities were either taken from the √ Γ 3 λ 5 h/ 5 . 10 30 . πhc 6 7 5 ø 2 5 2 3 5 13 17 3 = (ms) 15 ∼ = Duration dB λ sat ) I 2 1 7 7 7 54 54 26 67 16 32 . . . . sat ...... 1 1 1 1 I 2 2 6 1 0 8 (mW/cm K) rec 198 829 808 788 071 063 395 362 077 002 µ ...... T ( 0 0 0 0 7 6 2 0 4 2 π 2 234 956 956 956 872 872 765 065 626 029 / ...... Γ 5 5 5 5 5 5 9 6 1 5 (MHz) − − − − − − − − σ σ σ σ σ σ σ σ for four gray molasses pulses interspaced by free evolution lin ø ø ⊥ − − − − − − − − Laser + + + + + + + + lin Six-beam Six-beam Six-beam Six-beam Six-beam Six-beam Six-beam Six-beam σ σ σ σ σ σ σ σ Four-beam toms, metastable helium and chromium. The results presente P.S.D. configuration ra database [43] or from the reference data compiled on Danie al 2 2 with the thermal de Broglie wavelength / / 3 dB = 2 = 2 = 2 = 7 = 3 = 2 = 2 = 2 ′ ′ ′ ′ ′ ′ ′ ′ nλ , F , F , F , F , F , F , F , F 2 2 2 2 2 2 2 2 = / / / / / / / / 1 3 1 3 1 1 1 1 1 P P P P P P P P P 2 3 2 2 2 2 2 2 2 2 P 7 2 1 → → → → → → → → . Saturating intensities are obtained with the relation P.S.D. → → 2 2 D 2 / / 3 1 λ = 3 = 2 = 2 = 2 = 2 = 2 2 S S B 7 3 h Transition = 9 = 3 , F , F , F , F , F , F 2 mk 2 2 2 2 2 2 / / / / / / , F , F 1 1 1 1 1 1 2 2 = / / S S S S S S 1 1 2 2 2 2 2 2 S S 2 1 2 rec 1 1 1 2 2 T D D D D D D 1 1 D D [20] [41] [39] [23] [40] [40] [40] [37] [19] [42] [21] [38] [22] Paper Rosi 1999 2013 2013 2015 2015 2015 2016 2014 2015 2013 2016 2018 2015 Nath Colzi Chen Grier Triché This paper Sievers Sievers Sievers Bouton Salomon Tarnowski Burchianti ∗ Cs K K K Rb Cr Li Li Na He 6 7 39 40 41 When using the compression scheme. 87 52 23 4 133 * (Boson) (Boson) (Boson) (Boson) (Boson) (Boson) (Boson) (Boson) Element (Fermion) (Fermion) TABLE I. Statetemperatures. of Linewidths the were art taken for from NIST grey atomic molasses spect cooling of alkali a are obtained using the relation cited papers or calculated using the relation a single molasses pulse without the compression part. The fin 9

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