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We use a Feshbach resonance to tune the scattering length a of a Bose-Einstein condensate of 7Li in the |F=1,mF=1> state. Using the spatial extent of the trapped condensate, we extract a over a range spanning 7 decades from small attractive interactions to extremely strong repulsive interactions. The shallow zero crossing in the wing of the Feshbach resonance enables the determination of a as small as 0.01 Bohr radii. Evidence of the weak anisotropic magnetic dipole interaction is obtained by comparison with different trap geometries for small a.

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.

We excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior. Collective excitation of a Bose-Einstein condensate (BEC) is an essential diagnostic tool for investigating properties of the ultracold quantum state. Fundamental information about condensate dynamics can be determined from observations of collective modes [1][2][3], including the effects of temperature [4][5][6], and the dimensionality of the system [7]. In addition, the interplay between these modes and external agents, such as random potentials [8,9], lattices [10,11], as well as other atoms [12][13][14][15][16], can be investigated. Examining the excitation spectrum of the BEC allows for a detailed comparison with theoretical models [17][18][19][20] and related quantum systems such as superfluid helium [21,22] and superconductors [23,24].Generically, a collective excitation is generated by the modification of the trapping potential of the condensate [25]. One convenient method is to apply a sudden magnetic field gradient, thereby shifting the center of the trap and exciting a dipole oscillation about the trap center. One may also suddenly change the curvature of the trap to excite quadrupole modes. The lowest-lying m = 0 quadrupole mode is characterized by out-of-phase axial and radial oscillations.If the condensate is not the only occupant of the trap (i.e., there exists a thermal component or another species of atoms) then the other atoms may also be excited through these processes. The evolution of a collective excitation can therefore be complicated because the multiple components may affect damping or induce frequency shifts of the oscillation [12][13][14][15][16]. Therefore, modulating the trap, although an extremely useful tool for an isolated condensate, can be cumbersome when the system to be studied is multispecied. An alternative approach is to excite the condensate alone, leaving the other occupants of the trap untouched.In this work, we demonstrate the excitation of the lowestlying quadrupole mode in a BEC of 7 Li by modulating the atomic scattering length via a magnetic Feshbach resonance. In contrast to abruptly changing the scattering length [26], sinusoidal modulation enables the controlled excitation of a single mode at a specific frequency. In addition, by using this method, a coexisting thermal component will be minimally excited by the mean-field coupling to the normal gas [27,28]. In the case of a multispecies experiment, resonant modulation of the scattering length of one species will not necessarily excite the others, depending on the details of other F...

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.