Birth of a quasi-stationary black hole in an outcoupled Bose-Einstein condensate

TL;DR

This paper investigates how to create a stable sonic black hole in a Bose-Einstein condensate by outcoupling atoms through an optical lattice, analyzing protocols for long-term stationarity and deriving related analytical formulas.

Contribution

It demonstrates that optical lattices are more effective than single barriers for forming quasi-stationary sonic black holes and provides analytical insights into the horizon location and Hawking temperature.

Findings

Optical lattices outperform single barriers in creating stationary flows.

The sonic horizon is located at the envelope maximum of the optical lattice.

An analytical formula for Hawking temperature is derived.

Abstract

We study the evolution of an initially confined atom condensate which is progressively outcoupled by gradually lowering the confining barrier on one side. The goal is to identify protocols that best lead to a quasi-stationary sonic black hole separating regions of subsonic and supersonic flow. An optical lattice is found to be more efficient than a single barrier in yielding a long-time stationary flow. This is best achieved if the final conduction band is broad and its minimum not much lower than the initial chemical potential. An optical lattice with a realistic Gaussian envelope yields similar results. We analytically prove and numerically check that, within a spatially coarse-grained description, the sonic horizon is bound to lie right at the envelope maximum. We derive an analytical formula for the Hawking temperature in that setup.