Unruh and analogue Unruh temperatures for circular motion in 3+1 and 2+1 dimensions

Abstract

The Unruh effect states that a uniformly linearly accelerated observer with proper acceleration a experiences Minkowski vacuum as a thermal state in the temperature T lin = a/(2π), operationally measurable via the detailed balance condition between excitation and de-excitation probabilities. An observer in uniform circular motion experiences a similar Unruh-type temperature T circ , operationally measurable via the detailed balance condition, but T circ depends not just on the proper acceleration but also on the orbital radius and on the excitation energy. We establish analytic results for T circ for a massless scalar field in 3 + 1 and 2 + 1 spacetime dimensions in several asymptotic regions of the parameter space, and we give numerical results in the interpolating regions. In the ultrarelativistic limit, we verify that

Interferometric Unruh Detectors for Bose-Einstein Condensates

“…Formula 14is obtained from (1) by using for a the circular motion proper acceleration in the effective BEC Minkowski geometry and adjusting the energies to be defined with respect to the laboratory time, as is appropriate for the BEC. The actual effective temperature for circular motion includes an energydependent factor of order unity [25,27,40], which we shall suppress here; a thorough analysis of this order unity factor in (2 + 1) and (3 + 1) dimensions is given in our companion paper [41].…”

The Unruh Effect in Slow Motion

“…However, our linear setup can overcome some of the limitations of the circular proposals as we will note later. The key difference between such circular proposals and our proposal is that circular trajectories yield final probe temperatures which depend not just on the circular acceleration but also on the probe's speed and energy gap [36]. In our proposal, as we will see, this does not happen.…”

“…In this regard, our approach has some similarities to several circular Unruh effect proposals [29][30][31][32][33][34][35][36] in which the probe follows a circular trajectory. In these proposals, as in ours, the probe's acceleration has a constant magnitude but a changing direction.…”

Coherently amplifying photon production from vacuum with a dense cloud of accelerating photodetectors

“…In particular, Bell and Leinass [6] interpreted the observed spin depolarization of electron(s) undergoing uniform circular motion in a storage ring in terms of 'heating' by vacuum fluctuations (see also Refs. [7,8]). And Schutzhold et al [9] showed that oscillating electrons emit both classical (Larmor) and quantum radiation, with the latter corresponding to the accelerating electrons converting quantum vacuum fluctuations into entangled photon pairs.…”