Collective excitations of a trapped Bose-Einstein condensate in the presence of weak disorder and a two-dimensional optical lattice

TL;DR

This paper studies how weak disorder and a 2D optical lattice affect the collective excitations of a trapped Bose-Einstein condensate, revealing disorder's impact on phonons and surface modes during dimensional crossover.

Contribution

It generalizes hydrodynamic equations for a BEC in a 2D lattice with disorder and provides analytical results beyond mean-field theory, highlighting disorder's role in excitation dynamics.

Findings

Disorder influences collective excitation frequencies.

Effects on phonon propagation and surface modes are characterized.

Analytical results extend understanding of BEC excitations in complex potentials.

Abstract

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 dimensional crossover. In particular, consequences of disorder on the phonon propagation and surface modes are analyzed in detail. The experimental scenario is also proposed.