Superfluid Dynamics of a Bose-Einstein Condensate in a Periodic Potential

TL;DR

This paper explores the superfluid behavior of a Bose-Einstein condensate in a one-dimensional periodic potential, analyzing its properties through analytical and numerical methods, and identifying stability thresholds and effective mass effects.

Contribution

It introduces two density-dependent effective masses and group velocities, providing new insights into the superfluid dynamics and stability of BECs in periodic potentials.

Findings

Existence of sound waves in the Bogoliubov spectrum

Identification of energetic and dynamical instabilities at critical quasi-momenta

Dependence of oscillation frequencies on an effective mass averaged over the condensate density

Abstract

We investigate the superfluid properties of a Bose-Einstein condensate (BEC) trapped in a one dimensional periodic potential. We study, both analytically (in the tight binding limit) and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubov dispersion relation, and we introduce {\it two} different, density dependent, effective masses and group velocities. The Bogoliubov spectrum predicts the existence of sound waves, and the arising of energetic and dynamical instabilities at critical values of the BEC quasi-momentum which dramatically affect its coherence properties. We investigate the dependence of the dipole and Bloch oscillation frequencies in terms of an effective mass averaged over the density of the condensate. We illustrate our results with several animations obtained solving numerically the time-dependent Gross-Pitaevskii equation.