Measuring the entanglement of analogue Hawking radiation by the density-density correlation function

TL;DR

This paper proposes a method to measure entanglement in analogue Hawking radiation using density-density correlation functions, revealing energy-dependent entanglement properties and simplifying experimental detection.

Contribution

It introduces a practical approach to quantify Hawking radiation entanglement via density correlations, confirming previous numerical results and analyzing energy distribution effects.

Findings

Hawking radiation entanglement can be inferred from density-density correlations.

High energy tail of Hawking radiation is entangled, low energy part is not.

The method applies to cold systems where thermal phonons are negligible.

Abstract

We theoretically study the entanglement of Hawking radiation pairs emitted by an analogue black hole. We find that this entanglement can be measured by the experimentally accessible density-density correlation function, vastly simplifying the measurement. We find that while the Hawking radiation exiting the black hole might be Planck-distributed, the correlations between the Hawking radiation and the partner particles has a distribution which is weaker but broader than Planckian. Thus, the high energy tail of the distribution of Hawking radiation should be entangled, whereas the low energy part should not be. This confirms a previous numerical study. The full Peres-Horodecki criterion is considered, as well as a simpler criterion in the stationary, homogeneous case. Our method applies to systems which are sufficiently cold that the thermal phonons can be neglected.