## Packing rubidium into quantum degeneracy

When atomic gases, such as those of alkali elements, are cooled to very low temperatures, they can reach a state of quantum degeneracy, where their quantum nature comes to the fore. In this process, the very last step is evaporative cooling, in which the hottest atoms are coaxed into leaving the gas. Hu *et al.* devised a protocol that evades the evaporative cooling step, is faster, and suffers less atom loss. The method rests on iteratively manipulating the laser beams of an optical lattice in which a gas of ^{87}Rb atoms is held so that the gas becomes progressively denser. The method should be widely applicable to other atomic species.

*Science*, this issue p. 1078

## Abstract

Protocols for attaining quantum degeneracy in atomic gases almost exclusively rely on evaporative cooling, a time-consuming final step associated with substantial atom loss. We demonstrate direct laser cooling of a gas of rubidium-87 (^{87}Rb) atoms to quantum degeneracy. The method is fast and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of compression to increase the density, followed by Raman sideband cooling to decrease the temperature. From a starting number of 2000 atoms, 1400 atoms reach quantum degeneracy in 300 milliseconds, as confirmed by a bimodal velocity distribution. The method should be broadly applicable to many bosonic and fermionic species and to systems where evaporative cooling is not possible.

The ability to prepare quantum-degenerate Bose (*1*–*3*) and Fermi (*4*) gases has opened a multitude of research areas, including quantum simulation of complex Hamiltonians (*5*) and of quantum phase transitions (*6*). Quantum-degenerate gases are prepared in two steps: fast laser cooling until a certain density and temperature limit are reached, followed by slower evaporative cooling to Bose-Einstein condensation (BEC) or below the Fermi temperature. Compared with laser cooling, evaporative cooling (*1*–*4*) is slower; in addition, it requires favorable atomic collision properties, and only a small fraction of the original ensemble is left at the end of the process. The one exception to the two-step scheme is strontium (*7*), which features a very narrow optical transition. This enables the laser cooling of a thermal cloud in a large trap, while a small (1%) fraction of the ensemble undergoes BEC in a tighter, collisionally coupled trap. Previous attempts at laser cooling of other species, such as alkali atoms, stopped short of achieving BEC owing to two adverse effects that set in at high density: optical excitation of pairs of atoms at short distance, leading to light-induced loss (*8*, *9*), and reabsorption of emitted photons at high optical density, leading to excess recoil heating (*10*).

With respect to reaching quantum degeneracy, laser cooling techniques can be characterized in terms of the phase space density , which is the peak occupation per quantum state for a thermal cloud. Standard polarization gradient cooling (*11*) reaches . A considerable improvement is offered by Raman sideband cooling (RSC) (*12*–*14*), with which, by isolating the atoms from each other in a three-dimensional (3D) optical lattice, has been reached (*14*). Demagnetization cooling of chromium has also reached (*15*). A release-and-retrap compression approach (*16*) to increase the occupation in a 3D optical lattice attained, in combination with RSC, a record (*17*), limited by light-induced loss in doubly occupied lattice sites.

Here we show that by judicious choice of optical cooling parameters and trap geometry, it is possible to create a Bose condensate of ^{87}Rb atoms without any evaporation. Degenerate Raman sideband cooling (dRSC) (*13*) is performed with optical pumping light that is red-detuned by several hundred megahertz from the D_{1} atomic transition. We use release-and-retrap compression (*16*, *17*) 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, as observed through a bimodal velocity distribution.

The centerpiece of our setup is a square 2D optical lattice created by two orthogonal retroreflected beams, each with a power of 1.1 W and focused to an *e*^{–2} intensity waist of 18 μm at the atoms’ position (Fig. 1). The incoming beams are vertically polarized, whereas the polarizations of the reflected beams are rotated by θ = 80°. This induces a polarization gradient in the lattice that provides the required Raman coupling for dRSC (*13*). The two retroreflected beams provide a trap depth of *U*/*h* = 13 MHz each (where *h* is Planck’s constant), at an axial (tight) vibrational frequency of ω* _{xy}*/(2π) = 180 kHz and a radial vibration frequency along the vertical (

*z*) direction of kHz. [Here, ω

_{r2D}/(2π) = 4.5 kHz is the radial vibration frequency for a single 1D lattice beam.] A magnetic field

*B*= 0.23 G along

*z*is set to match the Zeeman splitting between the magnetic sublevels and to (where

*F*is the total angular momentum;

*m*, magnetic quantum number; , reduced Planck’s constant).

A cooling cycle consists of a Raman transition induced by the trapping light, which 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 λ_{t} = 1064 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 (*9*). To reduce this process relative to photon scattering by individual atoms (*18*), we use a σ^{–}-polarized optical pumping beam tuned below the D_{1} line away from photoassociation resonances (*9*, *15*). Because an excited atom can also decay to *F* = 1, we use bichromatic light with detunings Δ_{2}/(2π) = –630 MHz and Δ_{1}/(2π) = –660 MHz relative to the and transitions, respectively. This far-detuned D_{1}-line optical pumping configuration reduces light-induced inelastic collisions by at least an order of magnitude.

The experimental sequence starts by accumulating ^{87}Rb atoms in a magneto-optical trap, loading them into the 2D lattice by means of polarization gradient cooling (*16*), and applying dRSC for 100 ms. This prepares the atoms near the vibrational ground state in the strongly confined *x* and *y* directions [the kinetic energy measured by time-of-flight imaging is *K _{xy}*/

*h*= 50 kHz, close to (ω

*/4)/(2π) = 45 kHz], whereas in the vertical direction (*

_{xy}*z*), the atoms are cooled to

*T*≈ 12 μK (

_{z}*K*/

_{z}*h*= 120 kHz) through collisional thermalization between the axial and radial directions of the tubes. At this point, there are

*N*= 2000 atoms in the 2D lattice with a peak occupation of

*N*

_{1}≈ 1 atom per tube, corresponding to a peak phase space density and peak density

*n*

_{0}= 2.2 × 10

^{14}cm

^{–3}. To further increase

*n*

_{0}and , we apply release-and-retrap compression (

*16*) by adiabatically turning off (in 400 μs) the

*Y*trapping beam, so that the cloud shrinks in the

*y*direction thanks to the radial confinement of the

*X*trapping beam (Fig. 1C). After thermalization for 10 ms, the spatial extent of the cloud can be estimated by μm, where

*T*= 10 μK is the measured radial temperature,

_{z}*m*is the

^{87}Rb mass, and

*k*

_{B}is Boltzmann’s constant. The

*Y*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 (

*T*~ 50 μK), and we again apply dRSC for 100 ms. This yields again and

*T*= 12 μK, but at a peak occupation number of

_{z}*N*

_{1}= 6.9 atoms per tube for a total number

*N*= 1700 atoms. We repeat this procedure for the

*X*lattice beam and end up with

*N*= 1400 and

*N*

_{1}= 47 at a peak density

*n*

_{0}= 1 × 10

^{16}cm

^{–3}. At this point, the ensemble is below our optical resolution of 8 μm, and

*N*

_{1}is estimated from the measured temperatures in the corresponding 1D lattices and the separately measured trap vibration frequencies. Figure 2D shows the evolution of

*N*,

*N*

_{1}, and during the sequence that brings the system close to . We emphasize that evaporation is not occurring at any point because temperature reduction is only observed when the cooling light is on, and

*k*

_{B}

*T*≤ 0.1

*U*at all times.

When we subsequently apply the final dRSC stage for up to 100 ms, we observe the gradual appearance of a characteristic signature of condensate formation: a bimodal distribution of the velocity along the *z* direction that becomes more pronounced with longer dRSC time *t* (Fig. 2). A fit to the observed distribution for *t* = 80 ms with a single Gaussian curve yields a reduced χ^{2} = 137 (Fig. 2C), as opposed to χ^{2} = 0.91 for a bimodal distribution with a parabolic central component. (At *t = 5 *ms, the corresponding values are χ^{2} = 0.89 and χ^{2} = 0.75, respectively.) The bimodal distribution persists if we adiabatically turn off the *X* trap after cooling for *t* = 80 ms and observe the 2D gas in a 1D lattice (Fig. 2E).

In Fig. 3, we show the evolution of the kinetic energy, the bimodal distribution, and the atom number as a function of final-stage cooling time. Along the tightly confined directions, we cool to the vibrational ground state *K _{xy}*/

*h*= 50 kHz = 1.1 × (ω

*/4)/(2π), whereas along*

_{xy}*z*, we reach an average kinetic energy

*K*/

_{z}*h*= 120 kHz. Additionally, we observe only very limited atom loss (<5% at a peak density of

*n*

_{0}= 1 × 10

^{16}cm

^{–3}; inset in Fig. 3A), confirming that light-induced losses are strongly suppressed. Figure 3C shows the condensate fraction

*N*

_{0}/

*N*versus the calculated inverse phase space density (

*19*), where

*N*

_{0}is the number of condensed atoms. In the absence of a detailed 1D theory,

*N*

_{0}/

*N*is estimated as the fractional area under the narrower peak in the bimodal distribution. The onset of the bimodal distribution is observed near . In 1D systems, only a smooth crossover to a quantum-degenerate gas occurs (

*19*–

*21*), which is in agreement with our observation for

*N*

_{0}/

*N*. For our parameters, the system is in the crossover region between a weakly interacting 1D gas (

*22*) and a strongly interacting Tonks-Girardeau gas (

*23*,

*24*) (the calculated dimensionless interaction parameter is γ ≈ 2.7 at the peak local density), as well as in the crossover region between a 1D Bose gas and a 3D finite-size condensate (

*19*,

*25*). Although the character of the condensate is therefore ambiguous, the velocity distribution (Fig. 2) reveals a macroscopic population of the ground state.

Because 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 three-body loss, where the loss coefficient [*K* = 1.1 × 10^{–28} cm^{6} s^{–1} for a 3D thermal gas (*26*)] has been previously determined. In a 1D gas with γ ≈ 2.7, the three-body loss is strongly suppressed by a factor of ~100 (*27*, *28*), and indeed we do not detect any loss in the 1D tubes. Instead, we measure the three-body recombination in the 1D lattice (i.e., for a 2D gas), where we observe a lifetime of 300 ms; from this, we determine a peak density of 5.3 × 10^{14} cm^{–3} in the 2D gas, corresponding to a peak atom number of *N*_{1} ≥ 45 atoms per tube and a phase space density at the onset of quantum degeneracy (*19*), both in agreement with the previous estimation.

In our experiment, both the large red-detuning of the optical pumping light and the near-1D confinement observably reduce light-induced loss, whereas a photon-scattering rate below the trap vibration frequencies likely suppresses excess recoil heating in the festina lente regime (*10*, *29*). Although there is no known simple relation between the momentum distribution and the condensate fraction in the crossover regime in which our experiment operates, we estimate that up to 40% of the ensemble, or 550 atoms, are in macroscopically occupied ground states of 30 tubes with a peak occupation of 50 atoms per tube.

We expect that the number of atoms in the condensate can be substantially increased in the future by using higher trap power and that the method can be applied to various bosonic and 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 (*30*, *31*). Last, the fast preparation may pave the way for further studies of the strongly correlated Tonks gas regime (*23*, *24*).

## Supplementary Materials

This is an article distributed under the terms of the Science Journals Default License.

## References and Notes

**Acknowledgments:**This work was supported by the NSF, NSF Center for Ultracold Atoms, NASA, and Multidisciplinary University Research Initiative grants through the Air Force Office of Scientific Research and the Army Research Office. The authors gratefully acknowledge stimulating discussions with C. Chin, W. Ketterle, R. McConnell, and M. Zwierlein. The data presented in this paper are available upon request to J.H.