Local Quantum Thermometry using Unruh-De Witt detectors

TL;DR

This paper introduces a method to define and measure local temperature in quantum fields using Unruh-DeWitt detectors, revealing inhomogeneous temperature distributions in quantum systems on curved backgrounds.

Contribution

It provides an operational framework for local quantum temperature measurement and explores its implications in curved spacetime and ultracold atomic systems.

Findings

Local temperature varies in inhomogeneous quantum systems.

Observed temperature approaches zero as coupling vanishes.

Product of local temperature and log of local speed of light is approximately constant.

Abstract

We propose an operational definition for the local temperature of a quantum field employing Unruh-DeWitt detectors, as used in the study of the Unruh and Hawking effects. With this definition, an inhomogeneous quantum system in equilibrium can have different local temperatures, in analogy with the Tolman-Ehrenfest theorem from general relativity. We study the local temperature distribution on the ground state of hopping fermionic systems on a curved background. The observed temperature tends to zero as the thermometer-system coupling $g$ vanishes. Yet, for small but finite values of $g$, we show that the product of the observed local temperature and the logarithm of the local speed of light is approximately constant. Our predictions should be testable on ultracold atomic systems.