We have studied the effects of a disordered optical potential on the transport and phase coherence of a Bose-Einstein condensate ͑BEC͒ of 7 Li atoms. At moderate disorder strengths ͑V D ͒, we observe inhibited transport and damping of dipole excitations, while in time-of-flight images, random but reproducible interference patterns are observed. In situ images reveal that the appearance of interference is correlated with density modulation, without complete fragmentation. At higher V D , the interference contrast diminishes as the BEC fragments into multiple pieces with little phase coherence. The behavior of a superfluid or a superconductor in the presence of disorder is of fundamental interest. A superfluid can flow without friction around obstacles, and a superconductor can have zero resistance despite material defects. On the other hand, disorder is able to localize particles, resulting in an insulating state ͓1͔. Experimentally, disorder-induced superfluid/superconductor to insulator transitions ͑SIT͒ have been probed in many systems, including superfluid helium in porous media ͓2͔, thin-film and granular superconductors ͓3,4͔, and random Josephson junction arrays ͓5͔. While many believe that such a SIT is a quantum phase transition driven by quantum fluctuations, it remains a central task to understand exactly how the superfluid/superconducting order parameter, which consists both an amplitude and a phase, may be destroyed with increasing disorder. Numerous fundamental questions remain, such as the nature of the insulator, the fate of phase coherence throughout the transition, and the possibility of intermediate metallic phases ͓3,6,7͔.Cold atoms, with their intrinsic cleanliness coupled with remarkable controllability of physical parameters, have emerged as exceptional systems to study various condensed matter problems. Recently, several experiments ͓8-11͔ have studied 87 Rb condensates in random optical potentials and observed, for example, damping of collective excitations ͓8͔ and inhibition of expansion ͓9-11͔ due to disorder. Another experiment ͓12͔ has examined a Bose-Einstein condensate ͑BEC͒ in an incommensurate ͑quasirandom͒ optical lattice in order to investigate a possible "Bose-glass" phase ͓13͔. Experiments with disordered atomic quantum gases may provide unique insights into disordered quantum systems and may uncover a rich variety of quantum phases ͓14͔.Here we report experiments on a BEC of interacting 7 Li atoms subject to a well-controlled disordered potential. While we corroborate previous transport measurements ͓8-11͔, we have also probed the ground-state density distribution and phase coherence of the disordered BEC by performing both in situ and time-of-flight ͑TOF͒ imaging. While disorder inhibits transport of the BEC, reproducible TOF interference patterns are observed for intermediate disorder strengths V D , reflecting an underlying phase coherence in the disordered BEC. At stronger V D , the interference contrast diminishes as the BEC fragments into a "granular" condensate, which...

We investigate the effects of impurities, either correlated disorder or a single Gaussian defect, on the collective dipole motion of a Bose-Einstein condensate of 7 Li in an optical trap. We find that this motion is damped at a rate dependent on the impurity strength, condensate center-of-mass velocity, and interatomic interactions. Damping in the Thomas-Fermi regime depends universally on the disordered potential strength scaled to the condensate chemical potential and the condensate velocity scaled to the speed of sound. The damping rate is comparatively small in the weakly interacting regime, and, in this case, is accompanied by strong condensate fragmentation. In situ and time-of-flight images of the atomic cloud provide evidence that this fragmentation is driven by dark soliton formation.

Antiferromagnetism of ultracold fermions in an optical lattice can be detected by Bragg diffraction of light, in analogy to the diffraction of neutrons from solid-state materials. A finite sublattice magnetization will lead to a Bragg peak from the ( 1 2 1 2 1 2 ) crystal plane with an intensity depending on details of the atomic states, the frequency and polarization of the probe beam, the direction and magnitude of the sublattice magnetization, and the finite optical density of the sample. Accounting for these effects we make quantitative predictions about the scattering intensity and find that with experimentally feasible parameters the signal can be readily measured with a CCD camera or a photodiode and used to detect antiferromagnetic order.

We measure the effect of a magnetic Feshbach resonance (FR) on the rate and light-induced frequency shift of a photoassociation resonance in ultracold 7 Li. The photoassociation-induced loss-rate coefficient K p depends strongly on magnetic field, varying by more than a factor of 10 4 for fields near the FR. At sufficiently high laser intensities, K p for a thermal gas decreases with increasing intensity, while saturation is observed for the first time in a Bose-Einstein condensate. The frequency shift is also strongly field dependent and exhibits an anomalous blueshift for fields just below the FR.

We have used the narrow 2S 1/2 → 3P 3/2 transition in the ultraviolet (uv) to laser cool and magneto-optically trap (MOT) 6 Li atoms. Laser cooling of lithium is usually performed on the 2S 1/2 → 2P 3/2 (D2) transition, and temperatures of ∼300 μK are typically achieved. The linewidth of the uv transition is seven times narrower than the D2 line, resulting in lower laser cooling temperatures. We demonstrate that a MOT operating on the uv transition reaches temperatures as low as 59 μK. Furthermore, we find that the light shift of the uv transition in an optical dipole trap at 1070 nm is small and blueshifted, facilitating efficient loading from the uv MOT. Evaporative cooling of a two spin-state mixture of 6 Li in the optical trap produces a quantum degenerate Fermi gas with 3 × 10 6 atoms in a total cycle time of only 11 s. The creation of quantum degenerate gases using all-optical techniques [1-4] offers several advantages over methods employing magnetic traps. Optical potentials can trap any ground state, allowing selection of hyperfine sublevels with favorable elastic and inelastic scattering properties. In the case of Fermi gases, the ability to trap atoms in more than one sublevel eliminates the need for sympathetic cooling with another species [5,6], greatly simplifying the experimental setup. All-optical methods also facilitate rapid evaporative cooling since magnetically tunable Feshbach resonances can be employed to achieve fast thermalization.There are, however, challenges to all-optical methods. An essential prerequisite is an optical potential whose depth is sufficiently greater than the temperature of the atoms being loaded. The usual starting point is a laser cooled atomic gas confined to a magneto-optical trap (MOT). In a twolevel picture, atoms may be cooled to the Doppler limit T D =h /(2k B ), where /(2π ) is the natural linewidth of the excited state of the cooling transition [7,8]. In many cases, however, sub-Doppler temperatures can be realized due to the occurrence of polarization gradient cooling arising from the multilevel character of real atoms [9]. Polarization gradient cooling mechanisms are effective if the linewidth of the cooling transition is small compared to the hyperfine splitting of the excited state, or if there is a large degree of magnetic degeneracy in the ground state [10]. The limit to cooling in these cases is the recoil temperature T R =h 2 k 2 /(2mk B ), where k is the wave number of the laser cooling transition and m is the mass of the atom.Polarization gradient cooling is found to be efficient for most of the alkali-metal atoms including Na, Rb, and Cs; MOTs of these species routinely attain temperatures of ∼10 μK, which is not far above T R . Unfortunately, for Li and K, the elements most often employed in Fermi-gas experiments, sub-Doppler cooling is ineffective in the presence of magnetic fields, including those required for a MOT. For Li, sub-Doppler cooling is inhibited because the hyperfine splitting of the excited state is unresolved (Fig. 1), thus limiting ...