Spontaneous Excitation of an Accelerated Detector Interacting with a Massive Scalar Field and Unruh Effect

Abstract

We study spontaneous excitation of both a static detector (modelled by a two-level atom) immersed in a thermal bath and a uniformly accelerated one in the Minkowski vacuum interacting with a real massive scalar field. Our results show that the mass of the scalar field manifests itself in the spontaneous excitation rate of the static detector in a thermal bath (and in vacuum) in the form of a selection rule for transitions among states of the detector. However, this selection rule disappears for the accelerated ones, demonstrating that an accelerated detector does not necessarily behave the same as an inertial one in a thermal bath. We find the imprint left by the mass is the appearance of a grey-body factor in the spontaneous excitation and de-excitation rates, which maintains the detailed balance condition between them and thus ensures a thermal equilibrium at the Unruh temperature the same as that of the massless case. We also analyze quantitatively the effect of the mass on the rate of change of the detector's energy and find that when the mass is very small, it only induces a small negative correction. However, when it is very large, it then exponentially damps the rate, thus essentially forbidding any transitions among states of the detector.