Compressibility of a 3D Disordered Bose Lattice Gas

Philip Russ, Laura Wadleigh, Brian DeMarco

Russ, Phil, Yan, Mi, Kowalski, Nicholas +3 more

Disorder can be applied to transform conducting to insulating states by localizing individual quantum particles. The interplay between disorder and interactions in many-particle systems leads to a richer tapestry of quantum phase transitions. Here, we report the measurement in an ultracold lattice gas of a disorder-induced transition from a state with small disorder-independent compressibility to a state for which compressibility increases with disorder. At zero temperature this is the transition from a Mott insulator (MI) to a Bose glass (BG), both of which are insulating states. This transformation is observed using measurements of core compressibility. By determining how double occupancy changes with atom number, we identify the threshold disorder strength required to switch from disorder-independent MI-like to disorder-dependent BG-like compressible behavior.

Yansheng Zhang, Gevorg Martirosyan, C. J. Ho +3 more

Motivated by the experimental observation [1] that driving a non-interacting Bose gas in a 3D box with weak disorder leads to power-law energy growth, E ∝ t η with η = 0 . 46 ( 2 ) , and compressed-exponential momentum distributions that show dynamic scaling, we perform systematic numerical and analytical studies of this system. Schrödinger-equation simulations reveal a crossover from η ≈ 0 . 5 to η ≈ 0 . 4 with increasing disorder strength, hinting at the existence of two different dynamical regimes. We present a semi-classical model that captures the simulation results and allows an understanding of the dynamics in terms of an energy-space random walk, from which a crossover from E ∝ t 1 / 2 to E ∝ t 2 / 5 scaling is analytically obtained. The two limits correspond to the random walk being limited by the rate of the elastic disorder-induced scattering or the rate at which the drive can change the system’s energy. Our results provide the theoretical foundation for further experiments.

Toshiyuki Nishiyama, Masahisa Fukushima, Shokichi Kanno

Ying Hu, Zhaoxin Liang, Bambi Hu

We investigate the combined effects of weak disorder and a two-dimensional (2D) optical lattice on the collective excitations of a harmonically trapped Bose-Einstein condensate (BEC) at zero temperature. Accordingly, we generalize the hydrodynamic equations of superfluid for a weakly interacting Bose gas in a 2D optical lattice to include the effects of weak disorder. Our analytical results for the collective frequencies beyond the mean-field approximation reveal the peculiar role of disorder, interplaying with the 2D optical lattice and interatomic interaction, on elementary excitations along the 3D to 1D crossover. In particular, consequences of disorder on the phonon propagation and surface modes are analyzed in detail. The experimental scenario is also proposed.

N. M. Bogoliubov