Bogoliubov Theory of acoustic Hawking radiation in Bose-Einstein Condensates

TL;DR

This paper uses Bogoliubov theory to analyze quantum and thermal fluctuations in Bose-Einstein condensates with sonic horizons, providing analytical expressions for Hawking radiation spectra and correlations, validated by numerical calculations.

Contribution

It presents the first analytical derivation of Hawking radiation spectra and density correlations in Bose-Einstein condensates with a sonic horizon, including finite temperature effects.

Findings

Analytical spectra of Hawking radiation derived for step-like horizons.

Long-distance density correlations are enhanced by finite temperature.

Good agreement between analytical results and numerical simulations.

Abstract

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations.