On the existence of steady-state black hole analogues in finite quasi-one-dimensional Bose-Einstein condensates

TL;DR

This paper proposes a finite-size quasi-one-dimensional Bose-Einstein condensate with source and drain to sustain a stationary sonic black hole, analyzing its stability, quantum fluctuations, and signatures of Hawking radiation.

Contribution

It introduces a model for a steady-state black hole analogue in a finite BEC and examines its stability and quantum signatures, including Hawking radiation.

Findings

Existence of windows with infinite black hole lifetimes.

Validation of Bogoliubov theory for Hawking radiation signatures.

Identification of observable signatures of Hawking radiation in depleted condensate.

Abstract

We theoretically propose a finite-size quasi-one-dimensional Bose-Einstein condensate with coherent source and drain placed at its two ends, which can in principle sustain a stationary sonic black hole with a single event horizon. Our analysis is focused on the condensate persistence against quantum fluctuations. We show that similar to white hole-black hole pairs, dynamical instabilities occur. Investigating in detail the instabilities' dependence on the system parameters, we also identify windows of formally infinite black hole lifetimes. By using quantum depletion of the condensate as a diagnostic tool, we validate the usage of Bogoliubov theory to describe the analogue Hawking process, and establish novel signatures of Hawking radiation in the depleted cloud, both inside and outside the event horizon.