Dynamics of an elementary quantum system outside a radiating Schwarzschild black hole

Abstract

We study, in the framework of open quantum systems, the dynamics of a radially polarizable two-level atom in multi-polar coupling to fluctuating vacuum electromagnetic fields which is placed at a fixed radial distance outside a radiating Schwarzschild black hole, and analyze the transition rates between atomic energy levels and the steady state the atom is driven to. We find that the atom always thermalizes toward a steady state at an effective temperature between zero and the Hawking temperature of the black hole. Remarkably, the thermalization temperature depends on the transition frequency of the atom, so that atoms with different transition frequencies essentially thermalize to different temperatures. This counter-intuitive behavior is however in close analogy to what happens for a two-level atom in a stationary environment out of thermal equilibrium near a dielectric body of certain geometry and dielectric permittivity. Our results thereby suggest in principle a possible analogue system using engineered materials with certain desired dielectric properties to verify features of Hawking radiation in lab-top experiments.