Propagation of sound in a Bose Einstein condensate in an optical lattice

TL;DR

This paper investigates how sound propagates in a Bose-Einstein condensate within an optical lattice, revealing that lattice depth affects sound velocity and introduces novel phenomena like shock waves and amplitude saturation.

Contribution

It provides new insights into sound dynamics in optical lattices, highlighting nonlinear effects and phenomena absent in uniform condensates, supported by theoretical analysis.

Findings

Sound velocity decreases with increasing lattice depth

Shock waves can propagate slower than sound waves

Nonlinear corrections cause amplitude saturation

Abstract

We study the propagation of sound waves in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the velocity of propagation of sound wavepackets decreases with increasing optical lattice depth, as predicted by the Bogoliubov theory. The strong interplay between nonlinearities and the periodicity of the external potential raise new phenomena which are not present in the uniform case. Shock waves, for instance, can propagate slower than sound waves, due to the negative curvature of the dispersion relation. Moreover, nonlinear corrections to the Bogoliubov theory appear to be important even with very small density perturbations, inducing a saturation on the amplitude of the sound signal.