Damping of quasiparticles in a Bose-Einstein condensate coupled to an optical cavity

TL;DR

This paper develops a comprehensive theory to calculate the damping rates of density wave excitations in a Bose-Einstein condensate coupled to an optical cavity, highlighting resonant enhancements and mode interactions.

Contribution

It provides a detailed derivation of the resonant Beliaev damping enhancement and explores the strong coupling between polariton modes and phonon bath modes.

Findings

Resonant enhancement of damping occurs outside the critical region.

Large damping rates are associated with significant frequency shifts.

Strong coupling between polariton and collective phonon modes is revealed.

Abstract

We present a general theory for calculating the damping rate of elementary density wave excitations in a Bose-Einstein condensate strongly coupled to a single radiation field mode of an optical cavity. Thereby we give a detailed derivation of the huge resonant enhancement in the Beliaev damping of a density wave mode, predicted recently by K\'onya et al., Phys.~Rev.~A 89, 051601(R) (2014). The given density-wave mode constitutes the polariton-like soft mode of the self-organization phase transition. The resonant enhancement takes place, both in the normal and ordered phases, outside the critical region. We show that the large damping rate is accompanied by a significant frequency shift of this polariton mode. Going beyond the Born-Markov approximation and determining the poles of the retarded Green's function of the polariton, we reveal a strong coupling between the polariton and a collective mode in the phonon bath formed by the other density wave modes.