Phonon spectrum and correlations in a transonic flow of an atomic Bose gas

TL;DR

This paper analyzes phonon spectra and correlations in transonic atomic Bose gas flows, demonstrating near-thermal spectra and the effects of flow asymmetry on correlations, with implications for analog gravity experiments.

Contribution

It provides a detailed analysis of phonon spectra and correlations in transonic Bose gas flows, including the impact of flow asymmetry and horizon formation on observable quantities.

Findings

The phonon spectrum is nearly planckian near experimental parameters.

Flow asymmetry causes a finite shift in correlation locations.

Horizon formation modifies local and non-local density correlations.

Abstract

Motivated by a recent experiment of J.~Steinhauer, we reconsider the spectrum and the correlations of the phonons spontaneously emitted in stationary transonic flows. The latter are described by "waterfall" configurations which form a one-parameter family of stable flows. For parameters close to their experimental values, in spite of high gradients near the sonic horizon, the spectrum is accurately planckian in the relevant frequency domain, where the temperature differs from the relativistic prediction by less than $10 \%$. We then study the density correlations across the horizon and the non-separable character of the final state. We show that the relativistic expressions provide accurate approximations when the initial temperature is not too high. We also show that the phases of the scattering coefficients introduce a finite shift of the location of the correlations which was so far overlooked. This shift is due to the asymmetry of the flow across the horizon, and persists in the dispersion-less regime. Finally we show how the formation of the sonic horizon modifies both local and non-local density correlations.