We have performed pioneering investigations of a Bose-Einstein condensate in a random potential, produced by shining an optical speckle pattern onto the atoms. We have investigated both static and dynamic properties of the BEC in the presence of disorder. With small levels of disorder, stripes are observed in the expanded density profile and strong damping of dipole and quadrupole oscillations is seen. By studying the propagation of the BEC in a disordered waveguide, we have evidenced a strong suppression of mass transport as the speckle potential is increased. The experimental results are in good agreement with numerical calculations based on the Gross-Pitaevskii equation.

J. E. Lye et al.
Bose-Einstein Condensate in a Random Potential
Phys. Rev. Lett. 95, 070401 (2005)

C. Fort et al.
Effect of Optical Disorder and Single Defects on the Expansion of a Bose-Einstein Condensate in a One-Dimensional Waveguide
Phys. Rev. Lett. 95, 170410 (2005)

We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the quasimomentum state. This is unambiguously attributed to the onset of dynamical instability, after a comparison with the predictions of the Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid appearance of complex structures in the atomic density profile, as a consequence of the condensate phase uniformity breakdown.

L. Fallani et al.
Observation of Dynamical Instability for a Bose-Einstein Condensate in a Moving 1D Optical Lattice
Phys. Rev. Lett. 93, 140406 (2004)

We report the experimental observation of a lensing effect on a Bose-Einstein condensate expanding in a moving 1D optical lattice. The effect of the periodic potential can be described by an effective mass dependent on the condensate quasimomentum. By changing the velocity of the atoms in the frame of the optical lattice, we induce a focusing of the condensate along the lattice direction. The experimental results are compared with the numerical predictions of an effective 1D theoretical model. In addition, a precise band spectroscopy of the system is carried out by looking at the real-space propagation of the atomic wave packet in the optical lattice.

L. Fallani et al.
Optically Induced Lensing Effect on a Bose-Einstein Condensate Expanding in a Moving Lattice
Phys. Rev. Lett. 91, 240405 (2003)

We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wave function. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population, as well as the radial size of the expanding cloud are in good agreement with the predictions of theory.

P. Pedri et al.
Expansion of a Coherent Array of Bose-Einstein Condensates
Phys. Rev. Lett. 87, 220401 (2001)