# Induced density correlations in a sonic black hole condensate

## TL;DR

This paper models density correlations in a sonic black hole in a Bose-Einstein condensate, showing that atom-number fluctuations and quantum fluctuations together explain observed density correlation features.

## Contribution

It introduces a comprehensive model including both quantum and atom-number fluctuations to explain density correlations in sonic black holes.

## Key findings

- Quantum fluctuations alone partially explain the correlation features.
- Atom-number fluctuations alone can reproduce all observed features.
- Combined fluctuations yield the best agreement with experimental data.

## Abstract

Analog black/white hole pairs, consisting of a region of supersonic flow, have been achieved in a recent experiment by J. Steinhauer using an elongated Bose-Einstein condensate. A growing standing density wave, and a checkerboard feature in the density-density correlation function, were observed in the supersonic region. We model the density-density correlation function, taking into account both quantum fluctuations and the shot-to-shot variation of atom number normally present in ultracold-atom experiments. We find that quantum fluctuations alone produce some, but not all, of the features of the correlation function, whereas atom-number fluctuation alone can produce all the observed features, and agreement is best when both are included. In both cases, the density-density correlation is not intrinsic to the fluctuations, but rather is induced by modulation of the standing wave caused by the fluctuations.