# Analogue stochastic gravity phenomena in two-component Bose-Einstein condensates: Sound cone fluctuations

## TL;DR

This paper explores how quantum fluctuations in a two-component Bose-Einstein condensate can cause stochastic variations in sound propagation, serving as an analogue model for light cone fluctuations related to quantum gravity.

## Contribution

It introduces a coupled two-field model for BECs, derives an effective phononic theory, and analyzes sound cone fluctuations as analogue phenomena of quantum gravity effects.

## Key findings

- Quantum fluctuations induce measurable variations in sound travel time.
- The system models analogue light cone fluctuations in a controllable quantum gas.
- Proposed experiments could observe these stochastic sound cone effects.

## Abstract

We investigate the properties of the condensates of cold atoms at zero temperature in the tunable binary Bose-Einstein condensate system with a Rabi transition between atomic hyperfine states. We use this system to examine the effect of quantum fluctuations in a tunable quantum gas on phonon propagation. We show that the system can be represented by a coupled two-field model of a gapless phonon and a gapped mode, which are analogous to the Goldstone and Higgs particles in particle physics. We then further trace out the gapped modes to give an effective purely phononic theory using closed-time-path formalism. In particular, we are interested in the sound cone fluctuations due to the variation of the speed-of-sound acoustic metric, induced by quantum fluctuations of the gapped modes. These fluctuations can be interpreted as inducing a stochastic space-time, and thus are regarded as analogue phenomena of light cone fluctuations presumably arising from quantum gravity effects. The effects of fluctuations can be displayed in the variation in the travel time of sound waves. We suggest the relevant experiments to discuss the possibility of experimental observations.