Local quantum thermometry using Unruh–DeWitt detectors

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.

Zero mode suppression of superluminal signals in light-matter interactions

“…In that case, taking the principal branch of the logarithm, the oscillator contribution [φ osc (x),φ osc (x )] for both the periodic and Neumann boundary conditions in Eq. (25) and Eq. (30) appear to simplify further into…”

“…Consequently, by adding Eq. (25) or Eq. (30) to the zero mode commutator [φ zm (x),φ zm (x )], followed by the limit → 0, we get the following simple result for for spacelike separated x, x :…”

“…otherwise we will need to use the full expression given in Eq. (25). For arbitrary separation, using Eq.…”

“…In some contexts, such as UDW model coupled via derivative coupling, its effect can indeed be made negligible at the level of detector responses in appropriate limits [16], but in some other contexts it has significant impact on detector dynamics and entanglement [16,17,23,24]. There are also cases when the zero mode has been excluded by assumption from a setup with periodic boundary conditions (e.g., in [25][26][27][28][29]), thus it is of interest to further study the impact that the removal of the zero mode may have on the relativistic nature of the interaction, and in particular in the causality of the whole particle detector model.…”

Quantum entanglement in inhomogeneous 1D systems

“…Such relation between quantum entanglement and geometry helps explain thermal effects in quantum field theories studied on curved backgrounds, e.g. the Unruh effect where from the point of view of an accelerated observer, the temperature measured in a Minkowski vacuum must be proportional to its acceleration [8].…”