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 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 review recent studies of the effects of disorder on an atomic Bose-Einstein condensate (BEC). We focus particularly on our own experiments with 7 Li BECs in laser speckle. Both the interaction, which gives rise to the nonlinearity in a BEC, and the disorder can be tuned experimentally. This opens many opportunities to study the interplay of interaction and disorder in both condensed matter physics and nonlinear science.

Lithium-7 exhibits a broad Feshbach resonance that we exploit to tune the interactions in a Bose-Einstein condensate (BEC). We find that the rate of photoassociation can be enhanced by several orders of magnitude by tuning close to the resonance, and use this effect to observe saturation in the rate of association of a BEC for the first time. We have also used a lithium BEC to explore the effects of disorder on the transport and coherence properties of the condensate. We also show that the scattering length goes through a shallow zero-crossing far from the resonance, where it may be made positive or negative with a magnitude of less than 0.1 ao, and have made preliminary transport measurements in the regime of weak repulsive and attractive interactions.