High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices

TL;DR

This paper analyzes the propagation of high- and low-frequency phonon modes in dipolar Bose-Einstein condensate droplets within deep optical lattices, deriving dispersion relations and confirming them through simulations, with implications for experimental observations.

Contribution

It provides analytical derivations of phonon dispersion relations in dipolar BECs, including the optical-phonon branch dependent on dipole interactions, verified by simulations.

Findings

Optical-phonon branch exists only with dipole-dipole interactions.

Dispersion relations match direct simulation results.

Results applicable to real-time imaging of condensate dynamics.

Abstract

We study normal modes propagating on top of the stable uniform background in arrays of dipolar Bose-Einstein condensate (BEC) droplets trapped in a deep optical lattice. Both the on-site mean-field dynamics of the droplets and their displacement due to the repulsive dipole-dipole interactions (DDIs) are taken into account. Dispersion relations for two modes, \textit{viz}., high- and low- frequency counterparts of optical and acoustic phonon modes in condensed matter, are derived analytically and verified by direct simulations, for both cases of the repulsive and attractive contact interactions. The (counterpart of the) optical-phonon branch does not exist without the DDIs. These results are relevant in the connection to emerging experimental techniques enabling real-time imaging of the condensate dynamics and direct experimental measurement of phonon dispersion relations in BECs.