Density correlations and dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates

TL;DR

This paper develops a theoretical framework for understanding density correlations in atomic Bose-Einstein condensates caused by dynamical Casimir emission of phonon pairs during scattering length modulation, explaining recent numerical observations.

Contribution

It provides analytical expressions for density correlations in BECs under modulation and clarifies the physical mechanisms behind dynamical Casimir emission phenomena.

Findings

Analytical formulas for density correlations derived.

Identification of different modulation regimes affecting correlations.

Explanation of previously observed numerical features in Hawking radiation simulations.

Abstract

We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the dynamical Casimir emission of pairs of Bogoliubov phonons when the atom-atom scattering length is modulated in time. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical calculations of Hawking radiation from analog black holes.