Phonon Dynamics in Spherically-Curved Analog-Gravity Bose-Einstein Condensates

TL;DR

This paper investigates phonon behavior in a Bose-Einstein condensate designed to mimic a curved spacetime, analyzing classical wave propagation and quantum phonon creation during simulated universe expansion.

Contribution

It introduces a model of BECs with a curved spacetime metric, enabling study of phonon dynamics analogous to cosmological phenomena.

Findings

Sudden scale factor changes induce ripples in phonon waves.

Quantum phonon creation occurs during scale factor modifications.

Entanglement of created phonons is quantified.

Abstract

We study the low energy phonon dynamics of a Bose-Einstein condensate (BEC) with a density profile that is equivalent, via a coordinate transformation, to phonons traveling in a \lq\lq spherical\rq\rq\ curved spacetime that realizes the Friedman-Lema\^itre-Robertson-Walker (FLRW) metric. The metric of this BEC is characterized by its curvature $\kappa$ and a time-depdendent scale factor $a(t)$, with an increase in the latter corresponding to an expansion of the analog FLRW universe. We study the propagation of classical phonons in such BECs, finding that a sudden change in the scale factor induces ripples in the wave motion. In addition, we study quantum phonon creation (or vacuum amplification) due to the scale-factor modification and quantify their entanglement.