Defining an effective temperature and Bose–Einstein distribution for emitted photons

Determine whether, and under what conditions, an effective temperature and an associated Bose–Einstein distribution can be defined for the photon field emitted by circularly accelerated Unruh–DeWitt detectors inside a cylindrical cavity with Dirichlet boundary conditions, and, if such a definition is possible, specify the operational framework and conditions that make it valid.

Background

The paper proposes detecting the Unruh effect using Unruh–DeWitt detectors undergoing uniform circular motion inside a cylindrical cavity that enforces Dirichlet boundary conditions. By leveraging cavity mode selection, counter-rotating transitions, coherent-state stimulation, and Dicke-like superradiance, the authors show that the counter-rotating emission can dominate and become experimentally detectable at reduced accelerations.

While they define an equilibrium temperature for the atomic ensemble via the ratio of counter-rotating to rotating emission rates and show it can be negative, they explicitly note that the notion of an effective temperature for the emitted photons is more complicated. They state they cannot directly define such an effective temperature or a corresponding Bose–Einstein distribution and suggest it may be possible only under other conditions, identifying this as a topic for future work.