Observer dependence for the phonon content of the sound field living on the effective curved space-time background of a Bose-Einstein condensate

TL;DR

This paper explores how the particle content in quantum fields on curved space-time can be experimentally studied using a Bose-Einstein condensate and an Atomic Quantum Dot detector, revealing different responses for various effective space-times.

Contribution

It provides an experimental framework to investigate observer dependence of phonon content in curved space-time analogs within Bose-Einstein condensates.

Findings

Detector response varies with different effective space-times.

Responses are finite, nonstationary, vanishing, or thermal depending on the space-time.

Experimental method links quantum field theory in curved space to ultracold atom systems.

Abstract

We demonstrate that the ambiguity of the particle content for quantum fields in a generally curved space-time can be experimentally investigated in an ultracold gas of atoms forming a Bose-Einstein condensate. We explicitly evaluate the response of a suitable condensed matter detector, an ``Atomic Quantum Dot,'' which can be tuned to measure time intervals associated to different effective acoustic space-times. It is found that the detector response related to laboratory, ``adiabatic,'' and de Sitter time intervals is finite in time and nonstationary, vanishing, and thermal, respectively.