Violation of Cauchy-Schwarz inequalities by spontaneous Hawking radiation in resonant boson structures

TL;DR

This paper demonstrates that spontaneous Hawking radiation in resonant boson structures can violate classical Cauchy-Schwarz inequalities, serving as a clear signature of quantum effects in sonic black holes, with potential experimental detection.

Contribution

It analyzes the degree of Cauchy-Schwarz violation in Hawking radiation spectra from resonant boson structures, introducing new insights into quantum signatures in sonic black holes.

Findings

CS violation is largest near radiation spectrum peaks

Maximum violation temperature depends on structure parameters

Direct atom counting can observe CS violation in experiments

Abstract

The violation of a classical Cauchy-Schwarz (CS) inequality is identified as an unequivocal signature of spontaneous Hawking radiation in sonic black holes. This violation can be particularly large near the peaks in the radiation spectrum emitted from a resonant boson structure forming a sonic horizon. As a function of the frequency-dependent Hawking radiation intensity, we analyze the degree of CS violation and the maximum violation temperature for a double barrier structure separating two regions of subsonic and supersonic condensate flow. We also consider the case where the resonant sonic horizon is produced by a space-dependent contact interaction. In some cases, CS violation can be observed by direct atom counting in a time-of-flight experiment. We show that near the conventional zero-frequency radiation peak, the decisive CS violation cannot occur.