Low frequency analogue Hawking radiation: The Bogoliubov-de Gennes model

TL;DR

This paper analytically investigates the low-frequency behaviour of analogue Hawking radiation in Bose-Einstein condensates, revealing conditions that enhance the observability of quantum entanglement despite greybody effects.

Contribution

It provides analytical expressions for scattering coefficients and greybody factors in one-dimensional flows, highlighting how conformal coupling can reduce greybody effects and aid entanglement detection.

Findings

Hawking effect dominates at low frequencies in Bose-Einstein condensates.

Greybody factors can be significantly decreased under conformal coupling.

Reducing greybody factors facilitates entanglement observation at finite temperatures.

Abstract

We analytically study the low-frequency properties of the analogue Hawking effect in Bose-Einstein condensates. We show that in one-dimensional flows displaying an analogue horizon, the Hawking effect is dominant in the low-frequency regime. This happens despite non vanishing greybody factors, that is, the coupling of the Hawking mode and its partner to the mode propagating with the flow. To show this, we obtained analytical expressions for the scattering coefficients, in general flows and taking into account the full Bogoliubov dispersion relation. We discuss the obtained expressions for the greybody factors. In particular, we show that they can be significantly decreased if the flow obeys a conformal coupling condition. We argue that in the presence of a small but non-zero temperature, reducing greybody factors greatly facilitates the observation of entanglement, that is, establishing that the state of the Hawking mode and its partner is non-separable.