Creation of a Bose-condensed gas of rubidium 87 by laser cooling

Creation of a Bose-condensed gas of rubidium 87 by laser cooling

Jiazhong Hu    Alban Urvoy    Zachary Vendeiro    Valentin Crépel    Wenlan Chen    Vladan Vuletić Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Abstract

We demonstrate direct laser cooling of a gas of rubidium 87 atoms to quantum degeneracy. The method does not involve evaporative cooling, is fast, and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of cloud compression to increase the density, followed by degenerate Raman sideband cooling to decrease the temperature. Light-induced loss at high atomic density is substantially reduced by using far red detuned optical pumping light. Starting with 2000 atoms, we prepare 1400 atoms in 300 ms at quantum degeneracy, as confirmed by the appearance of a bimodal velocity distribution as the system crosses over from a classical gas to a Bose-condensed, interacting one-dimensional gas with a macroscopic population of the quantum ground state. The method should be broadly applicable to many bosonic and fermionic species, and to systems where evaporative cooling is not possible.

thanks: These two authors contributed equally.thanks: These two authors contributed equally.

The ability to prepare quantum degenerate Bose Anderson et al. (1995); Bradley et al. (1995); Davis et al. (1995) and Fermi DeMarco and Jin (1999) gases has opened up a multitude of research areas, including quantum simulation of complex Hamiltonians Bloch et al. (2012) and quantum phase transitions Madison et al. (2001); Sondhi et al. (1997). Quantum degenerate gases are prepared in two steps: fast laser cooling until a certain density and temperature limit is reached, followed by slower evaporative cooling to Bose-Einstein condensation (BEC) or below the Fermi temperature. Compared to laser cooling, evaporative cooling Ketterle and Druten (1996) is slower, requires favorable atomic collision properties (a large ratio of elastic to inelastic collisions), and only a small fraction of the original ensemble is left at the end of the process. The one exception to this scheme is strontium Stellmer et al. (2013), which features a very narrow optical transition. The narrow line enables the laser cooling of a thermal cloud in a large optical trap, while a small fraction of the ensemble undergoes BEC in a tighter, collisionally coupled trap.

Previous attempts at laser cooling all other species, and especially the alkali workhorse atoms, directly to quantum degeneracy have been limited by light-induced collisions Walker and Feng (1994); Burnett et al. (1996) that result in substantial heating and loss at the atomic densities required for condensation. With respect to reaching quantum degeneracy, the various laser cooling techniques can be characterized in terms of the attainable phase space density , which is the peak occupation per quantum state for a thermal cloud. Standard polarization gradient cooling Dalibard and Cohen-Tannoudji (1989) reaches values of . A significant improvement of several orders of magnitude is offered by Raman sideband cooling (RSC) Hamann et al. (1998); Vuletić et al. (1998); Kerman et al. (2000), where by keeping the atoms isolated from each other in a three-dimensional (3D) optical lattice, has been reached Kerman et al. (2000). In chromium, a demagnetization cooling technique has also reached Rührig et al. (2015). Weiss and co-workers pioneered a release-and-retrap compression approach to increase the occupation in a 3D optical lattice DePue et al. (1999), and, in combination with RSC, attained a record Han et al. (2000), limited by light-induced inelastic collisions in doubly occupied lattice sites.

Figure 1: Experimental scheme and procedure. A Rb atoms are trapped in a 2D lattice formed by two orthogonal retroreflected trapping beams at 1064 nm. The cooling light at 795-nm propagates along the magnetic field (), and is -polarized. B Simplified atomic level structure for dRSC. The Zeeman splitting between two magnetic sublevels is matched to the vibrational splitting in the tightly confined direction. C Release-and-retrap compression sequence used to increase the atomic density. Starting from a sparsely filled 2D lattice, we perform dRSC (I) and then switch off the Y trapping beam to compress the atoms along y in the X trapping beam (II). After a short thermalization time we switch back to the 2D lattice with an increased occupation number per trap (III). The procedure is repeated for the X beam to compress the atoms into a small number of tubes (IV). A final dRSC in this system (V) then yields a condensate.

In this Report we show that it is possible to reduce light-induced atom loss and create a Bose condensate by laser cooling Rb, without any evaporation. This is achieved by using far-detuned optical pumping light in degenerate Raman sideband cooling (dRSC) Vuletić et al. (1998). Inelastic atom-atom collisions are further reduced in a 2D lattice geometry with near one-dimensional confinement. We use release-and-retrap compression DePue et al. (1999); Han et al. (2000) to strongly increase the atomic density after each optical cooling cycle. Starting with 2000 atoms in the central trapping region, we reach quantum degeneracy in 300 ms with 1400 atoms. In the future, higher trap power should yield significantly larger ensembles, as it is now the limiting factor for the atom number.

The centerpiece of our setup is a square 2D optical lattice using two retroreflected beams arranged orthogonally to one another, each with a power of 1.1 W. All beams are focussed to an intensity waist of 18 m at the position of the atoms. The incoming beams are vertically polarized, while the polarizations of the reflected beams are rotated by . This induces a polarization gradient in the lattice that provides the required Raman coupling for dRSC Vuletić et al. (1998). For each 1D optical lattice, the trap depth is  MHz, the axial (tight) vibrational frequency is  kHz, and the radial vibrational frequency is  kHz. In the 2D lattice with the two beams combined, this yields  kHz along the weakly confined direction. A magnetic field  G, applied along the vertical propagation direction of the optical pumping beam, is set to match the Zeeman splitting between the magnetic sublevels and to .

A cooling cycle consists of a Raman transition induced by the trapping light, that removes one vibrational quantum in the tightly confined direction (Fig. 1B), followed by optical pumping back to . This reduces an atom’s motional energy by per optical pumping cycle. The very far detuned trap light that drives the Raman transition (wavelength  nm) does not produce any appreciable atom loss, but the optical pumping can induce inelastic binary collisions as an atom pair is excited to a molecular potential that accelerates the atoms before they decay back to the ground state Burnett et al. (1996). To suppress this process Vuletić et al. (1999), we use a -polarized optical pumping beam tuned below the line to a local loss minimum in between photoassociation resonances Burnett et al. (1996); Rührig et al. (2015). Since an excited atom can also decay to , we use bichromatic light with detunings  MHz and  MHz relative to the and transitions, respectively. This modified optical pumping configuration represents the most significant improvement over earlier schemes Han et al. (2000); Kerman et al. (2000); Vuletić et al. (1998); Hamann et al. (1998), and we find that light-induced inelastic collisions are suppressed by at least an order of magnitude.

Figure 2: A to C: Bimodal velocity distribution emerging during the final laser cooling stage indicating macroscopic population of the ground state. Observed optical depth (OD) along after a ballistic expansion of 1.3 ms for cooling times of 5 ms (A), 20 ms (B) and 80 ms (C), averaged over 200 repetitions of the experiment. The red lines show Gaussian fits to the wings of the distributions, and green lines are quadratic fits to the remaining distribution in the center. Here the intensity of the trapping beams is ramped down in 400 s, slowly with regard to the axial trapping frequency but rather quickly with regard to the motion along , in order to reduce the interaction energy. D: Evolution of the total atom number (blue) or atom number per lattice tube (red), vs the phase space density during the sequence, with the steps labeled I to V as defined in Fig. 1B. The solid lines represent the dRSC process and the dotted lines represent the spatial compression. Each cooling step enhances by one order of magnitude, then the release-and-retrap compression increases the peak occupation number while slightly decreasing . E: Velocity distribution along for the same parameters as in C, but observed for a 2D gas after releasing the atoms into the 1D lattice Y.
Figure 3: A Cooling performance in the final stage. Average kinetic energy in the directions of strong (blue) and weak (red) confinement against cooling time. After 80 ms of cooling, the atoms are in the vibrational ground state of the axial direction. The inset shows that there is almost no atom loss during the final cooling stage. The loss suppression is due to far-red-detuned optical pumping and the 1D geometry. B Condensate fraction vs cooling time. In A and B the dashed lines are exponential fits shown as a guide to the eye. C Condensate fraction vs the inverse peak phase space density . The blue line is the theoretical prediction for an ideal gas of 50 atoms in a 1D trap Ketterle and van Druten (1996), shown as a guide to the eye.

The experimental sequence starts by accumulating cold Rb atoms in a magneto-optical trap, loading them into the 2D lattice using polarization gradient cooling DePue et al. (1999), and cooling them for 100 ms with dRSC. This prepares the atoms near the vibrational ground state in the strongly confined and directions (the kinetic energy upon instantaneous trap release is 50 kHz, close to  kHz), while in the vertical direction () the atoms are cooled to  K ( kHz) via collisional thermalization between the axial and radial directions of the tubes. At this point there are atoms in the 2D lattice with a peak occupation of atom per tube, corresponding to a peak phase space density , and peak density  cm. In order to further increase the density and , we apply release-and-retrap compression DePue et al. (1999) by adiabatically turning off (in 400 s) the Y trapping beam, such that the cloud shrinks in the direction due to the radial confinement of the X beam (Fig. 1C). After thermalization for 10 ms, the spatial extent of the cloud can be estimated by m, where K is the measured radial temperature, is the atomic mass of Rb, and is Boltzmann’s constant. The lattice beam is then turned back on in 1 ms. This loads the compressed ensemble back into a 2D lattice, resulting in a higher temperature ( K), and we apply again dRSC for 100 ms. This yields again , 12 K, but at a peak occupation number of atoms per tube for a total atom number . We repeat this procedure for the X lattice beam and end up with and at a peak density cm. At this point the trapped atom ensemble is below our optical resolution limit of 8 m, and is estimated from the measured temperatures in the corresponding 1D lattices, and the separately measured trap vibration frequencies. Fig. 2D shows the evolution of , and during the sequence that brings the system close to . We would like to emphasize that evaporation is not occurring at any point, since temperature reduction is only observed when the cooling light is on, and at all times.

When we then apply the final dRSC stage for up to 100 ms, we observe the gradual appearance of a characteristic signature of condensate formation, a bimodal velocity distribution along the direction that becomes more pronounced with longer dRSC time (Fig. 2). If we attempt to fit the observed distribution for  ms with a single Gaussian curve, the reduced is (Fig. 2C), as opposed to for a bimodal distribution with a parabolic density component in the center. (At  ms, the corresponding values are and , respectively.) The bimodal distribution persists if we adiabatically turn off the X trap after cooling for  ms and observe the 2D gas in a 1D lattice (Fig. 2E).

In Fig. 3, we show the evolution of the kinetic energy, the condensate fraction, and the atom number as a function of cooling time for the final cooling stage. Along the tightly confined direction, we reach  kHz , indicating cooling to the vibrational ground state. Along the vertical, weakly confined direction, we reach an average kinetic energy  kHz. Additionally, we observe only very limited atom loss ( at a peak density of cm, inset to Fig. 3A), confirming that light-induced losses are strongly suppressed. (For the initial two cooling stages, we observe a similar temperature evolution at a slightly smaller loss.) Fig. 3C also shows the condensate fraction , defined as the fractional area under the narrower peak in the bimodal distribution, vs the calculated inverse phase space density (see supplementary materials). Within an estimated systematic error of a factor of 2 for , the onset of the bimodal distribution is observed near . Note that in 1D systems, only a smooth crossover to a quantum degenerate gas occurs Petrov et al. (2000); Bouchoule et al. (2007), which is in agreement with our observation for the condensate fraction . For our parameters the system is at the same time in the crossover region between a weakly interacting 1D gas Krüger et al. (2010) and the strongly interacting Tonks-Girardeau gas Kinoshita et al. (2004); Paredes et al. (2004) (the calculated dimensionless interaction parameter is at the peak local density), as well as in the crossover region between a 1D Bose gas and a 3D finite-size condensate Görlitz et al. (2001) (see supplementary materials). While the exact character of the condensate is therefore ambiguous, the velocity distribution (Fig. 2) clearly reveals a macroscopic population of the ground state at quantum degeneracy.

Since the atomic cloud is below our optical resolution, the atomic density cannot be directly determined through optical imaging. However, an independent verification is possible by measuring 3-body loss, where the loss coefficient ( cms for a 3D thermal gas Söding et al. (1999)) has been previously determined. It is known that 3-body loss is strongly suppressed in a 1D gas for Tolra et al. (2004); Haller et al. (2011), and indeed we do not detect any loss in the 1D tubes. Instead, we measure the 3-body recombination in the 1D lattice, i.e. for a 2D gas, where we observe a three-body recombination timescale of 300 ms, from which we determine a peak density of  cm in the 2D gas, corresponding to a peak atom number of atoms per tube for the 1D ensembles. This is in agreement with the previous estimation, and yields a phase space density at the onset of quantum degeneracy.

In conclusion, we have directly laser cooled a gas of alkali atoms to quantum degeneracy, which had remained an elusive goal since the early quest for BEC. We expect that the atom number can be substantially increased in the future using higher trap power, and that the method can be applied to various bosonic as well as fermionic atomic species, potentially even under conditions where evaporative cooling is impossible. The far-detuned optical pumping light may also enable atom-number resolving measurements in quantum gas microscopes Bakr et al. (2009); Sherson et al. (2010). Finally, the fast preparation may pave the way for further studies of the nature and coherence properties of the condensate at the boundary between 3D and 1D, and into the strongly correlated Tonks gas regime Kinoshita et al. (2004); Paredes et al. (2004).

This work was supported by the NSF, NSF CUA, NASA and MURI grants through AFOSR and ARO. The authors gratefully acknowledge stimulating discussions with Cheng Chin, Wolfgang Ketterle, Robert McConnell and Martin Zwierlein.

References

Supplementary materials: Raman sideband cooling of rubidium 87 to Bose-Einstein condensation

.1 Experimental details

The two trapping beams differ in frequency by 160 MHz to avoid interference effects and their powers can be independently controlled by separate acousto-optical modulators. The intensity of the optical pumping beam at 795 nm is set to an off-resonant scattering rate s, and the power ratio between the two frequency component is set to have a 3 times stronger scattering rate on the transition. This prevents the atoms that have decayed to the state from undergoing heating Raman transitions. The atoms are imaged after a time-of-flight of typically 1.3 ms via absorption imaging on the cycling transition of the D2-line, in the plane defined by the lattice beams, and at a 20 angle relative to the X lattice beams (see Fig. 1 of the main text). We summarize all relevant experimental parameters in Table 1.

trap wavelength 1064 nm
power of each trapping beam 1.1 W
waist 18 m
180 kHz
4.5 kHz
6.3 kHz
trap depth in the 1D lattice /h 13 MHz
magnetic field 0.23 G
MHz
MHz
Table 1: Experimental parameters.

.2 Estimation of the phase space density

We measure the kinetic energies and , and compare them to the trapping vibrational frequencies and . Hence, we estimate the relative ground state occupation along each direction when the chemical potential is zero. Assuming (, or ) is the temperature along direction with the vibrational frequency , the kinetic energy is related to by

(S1)

Then, we know the relative ground state occupation is

(S2)

The occupation of the 3D ground state is

(S3)

Thus the phase space density is calculated as

(S4)

here is the measured temperature along . is the measured kinetic energy along or , and is the peak atom number per lattice tube.

.3 Three-body recombination measurement

It was previously reported that three-body losses are strongly reduced in a one-dimensional cloud Tolra et al. (2004); Haller et al. (2011). Indeed we are not able to measure any significant three-body loss in the tubes. Therefore we measured the three-body recombination rate in a two-dimensional geometry by transferring the atoms to the Y optical lattice (i.e. by merging the tubes in the x direction) after the final cooling for 10 ms, and measuring the atom number as a function of the holding time (Fig. S1).

Figure S1: Atom number in the state as a function of the holding time in the Y lattice. The blue solid line is a fit to the analytic solution of the three-body loss decay, with an initial loss timescale of  ms.

By fitting the theoretical model for the three-body loss, we obtain an initial loss timescale of  ms. Assuming a thermal velocity distribution for the atoms and averaging over the Gaussian density profile in each trap and over the different lattice sites in the 1D lattice, we obtain the following relation between the initial peak density in the 2D gas and :

(S5)

Here we used the value  cms from Söding et al. (1999) as the three-body loss coefficient for the state for a classical (non-condensed) gas. This density is also consistent with the peak atom number per tube derived from the atomic temperature and trap vibrational frequencies.

.4 Detuning dependence of the cooling sequence

We also test a few different detuning for the optical pumping beam of dRSC. For each detuning setting, the laser intensity was adjusted to maintain a scattering rate of  s. When using exactly the same cooling sequence as described in the main text, we succeed to produce a condensate also at a the smaller detuning  MHz (Fig. S2C) but not at  MHz or  MHz (Fig. S2A-B).

Figure S2: Velocity distribution of the atoms along the Z direction after 80 ms of cooling in the final cooling stage, for various detunings of the cooling beam  MHz (A),  MHz (B) and  MHz (C), avaraged over 100 repetitions. The data is fitted with a bimodal distribution in the same way as in Fig. 2 of the main text.

.5 BEC regime

For our parameters, at the critical temperature for quantum degeneracy of , the system is at the boundary between a 3D gas and a 1D gas Görlitz et al. (2001). Furthermore, the dimensionless interaction parameter Petrov et al. (2000), where is the 1D density, and is the interaction strength for the 3D scattering length , for our system is at the peak 1D density. This means that the system is also at the boundary between a weakly interacting Thomas-Fermi gas (, for high linear density ) and a strongly correlated Tonks gas (, for low ) Petrov et al. (2000); Kinoshita et al. (2004); Paredes et al. (2004). In fact, the latter has been measured to exhibit substantially lower collisional loss due to the reduced correlation function Tolra et al. (2004); Haller et al. (2011). This effect may also help further reduce the light-induced loss during dRSC in the near-1D geometry.

Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
139175
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description