Sound waves in a backreaction-affected analogue spacetime: acoustic metric, mass, and correlations in Bose-Einstein condensates

Abstract

Analogue gravity treats sound as a field on an effective spacetime set by the background flow, but quantum fluctuations feed back on this background. Whether a condensate modified by such backreaction still defines a spacetime for the quantum field remains open. Using a number-conserving expansion of a Bose-Einstein condensate, we show that in the sound-wave and eikonal approximations the first-order phase fluctuation propagates on an acoustic metric of the backreaction-corrected condensate and acquires a spacetime-dependent mass that cannot be absorbed into the metric. For a finite, quasi-one-dimensional gas after an interaction quench, backreaction enhances the equal-point phase correlation by about $10\%$ in the bulk and up to $20\%$ near the walls while the depletion remains below $2\%$; the bulk enhancement survives finite imaging resolution.