Phonon redshift and Hubble friction in an expanding BEC

TL;DR

This paper derives an effective wave equation for phonons in an expanding ring-shaped Bose-Einstein condensate, revealing redshift and damping effects analogous to cosmological phenomena, and connects theoretical predictions with experimental results.

Contribution

It introduces an action-based dimensional reduction approach to model phonon dynamics in expanding BECs, highlighting redshift and damping effects similar to Hubble friction.

Findings

Phonon frequency redshifts with expansion rate

Amplitude of phonons damps proportionally to volume change

Results align with recent experimental observations

Abstract

We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon's direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by $\dot{\cal V}/{\cal V}$, where $\cal{V}$ is the volume of the background condensate. This behavior is analogous to the redshifting and "Hubble friction" for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.