The Quantum de Laval Nozzle: stability and quantum dynamics of sonic horizons in a toroidally trapped Bose gas containing a superflow

TL;DR

This paper investigates the stability and quantum dynamics of sonic horizons in a toroidally trapped Bose-Einstein condensate, demonstrating the presence of analogue Hawking radiation and instabilities through numerical and theoretical analysis.

Contribution

It introduces the quantum de Laval nozzle as a realistic system for studying black hole analogues and analyzes its stability and quantum effects using Bogoliubov theory and the truncated Wigner method.

Findings

Existence of stable black hole-white hole horizons in Bose gases.

Identification of dynamical instabilities linked to Hawking-like pair creation.

Confirmation of two-mode squeezing as a signature of analogue Hawking radiation.

Abstract

We study an experimentally realizable system containing stable black hole-white hole acoustic horizons in toroidally trapped Bose-Einstein condensates - the quantum de Laval nozzle. We numerically obtain stationary flow configurations and assess their stability using Bogoliubov theory, finding both in hydrodynamic and non-hydrodynamic regimes there exist dynamically unstable regions associated with the creation of positive and negative energy quasiparticle pairs in analogy with the gravitational Hawking effect. The dynamical instability takes the form of a two mode squeezing interaction between resonant pairs of Bogoliubov modes. We study the evolution of dynamically unstable flows using the truncated Wigner method, which confirms the two mode squeezed state picture of the analogue Hawking effect for low winding number.