Bogoliubov sound speed in periodically modulated Bose-Einstein condensates

TL;DR

This paper investigates the Bogoliubov excitations in Bose-Einstein condensates within optical lattices, focusing on phonon dispersion relations for both stationary and flowing condensates using systematic theoretical expansions.

Contribution

It provides a systematic derivation of the phonon dispersion relation in periodically modulated Bose-Einstein condensates, confirming previous hydrodynamic results for current-carrying states.

Findings

Derived the phonon dispersion relation via systematic expansion.

Confirmed agreement with hydrodynamic theory for current-carrying condensates.

Analyzed long wavelength phonon behavior in optical lattices.

Abstract

We study the Bogoliubov excitations of a Bose-condensed gas in an optical lattice. Of primary interest is the long wavelength phonon dispersion for both current-free and current-carrying condensates. We obtain the dispersion relation by carrying out a systematic expansion of the Bogoliubov equations in powers of the phonon wave vector. Our result for the current-carrying case agrees with the one recently obtained by means of a hydrodynamic theory.