Thermal and Nonthermal Signatures of the Unruh Effect in Casimir-Polder Forces

Abstract

We show that Casimir-Polder forces between two relativistic uniformly accelerated atoms exhibit a transition from the short distance thermal-like behavior predicted by the Unruh effect to a long distance nonthermal behavior, associated with the breakdown of a local inertial description of the system. This phenomenology extends the Unruh thermal response detected by a single accelerated observer to an accelerated spatially extended system of two particles, and we identify the characteristic length scale for this crossover with the inverse of the proper acceleration of the two atoms. Our results are derived separating at fourth order in perturbation theory the contributions of vacuum fluctuations and radiation reaction field to the Casimir-Polder interaction between two atoms moving in two generic stationary trajectories separated by a constant distance and linearly coupled to a scalar field. The field can be assumed in its vacuum state or at finite temperature, resulting in a general method for the computation of Casimir- Polder forces in stationary regimes

Thermal and nonthermal scaling of the Casimir-Polder interaction in a black hole spacetime

“…[22] (also notice similar studies in [24]), where the large-distance scaling of the Casimir interaction among two relativistic uniformly accelerated atoms was studied. Close to the event horizon, the Schwarzschild metric takes the form of the Rindler line element, and we find that the characteristic exponent of the algebraic scaling discussed in [22] is perfectly mirrored in the large interatomic separation scaling of the Casimir force close to the black hole. The nonthermal correction to the Casimir interaction is imprinted by the noninertial character of the background metric which becomes sizeable at distances larger than the inverse of the surface gravity of the black hole, that is, larger than 4GM/c 2 .…”

“…In Sec. III, we calculate the Casimir-Polder interaction energy for static atoms outside a Schwarzschild black hole and compare it with analogous results for relativistically uniformly accelerated atoms [22]. Conclusions and final remarks are given in Sec.…”

“…(3)(4) below and Refs. [22,23]) provide a set of general formulae to compute Casimir-Polder forces from first principles without resorting to specific phenomenological models.…”

“…The approach we use is the DDC formalism up to fourth order in perturbation theory, following closely Refs. [22,23]. In particular, we consider the contribution to the interaction energy coming from the interplay between vacuum fluctuations and radiation reaction among the two identical two-level atoms linearly coupled with the scalar field.…”

“…However, only recently the method by DDC has been extended to fourth order in perturbation theory for atoms linearly coupled to a scalar field [22,23], as necessary to compute the Casimir-Polder force between two polarizable, neutral atoms in their respective ground states.…”