Analogue Stochastic Gravity in Strongly-Interacting Bose-Einstein Condensates

TL;DR

This paper develops a quantum geometric theory of fluctuations in superfluid hydrodynamics, modeling phonons as a quantum bath and deriving stochastic equations akin to stochastic gravity, with potential physical implications.

Contribution

It introduces a quantum geometric framework for superfluid fluctuations, generalizing the two-fluid model and connecting to stochastic gravity concepts.

Findings

Derived Langevin equations coupling superfluid and phonons.

Formulated a fluctuation-dissipation theorem in geometric terms.

Discussed physical consequences of quantum fluctuations in superfluids.

Abstract

Collective modes propagating in a moving superfluid are known to satisfy wave equations in a curved space time, with a metric determined by the underlying superflow. We use the Keldysh technique in a curved space-time to develop a quantum geometric theory of fluctuations in superfluid hydrodynamics. This theory relies on a 'quantized' generalization of the two-fluid description of Landau and Khalatnikov, where the superfluid component is viewed as a quasi-classical field coupled to a normal component -- the collective modes/phonons representing a quantum bath. This relates the problem in the hydrodynamic limit to the 'quantum friction' problem of Caldeira-Leggett type. By integrating out the phonons, we derive stochastic Langevin equations describing a coupling between the superfluid component and phonons. These equations have the form of Euler equations with additional source terms expressed through a fluctuating stress-energy tensor of phonons. Conceptually, this result is similar to stochastic Einstein equations that arise in the theory of stochastic gravity. We formulate the fluctuation-dissipation theorem in this geometric language and discuss possible physical consequences of this theory.