Transitions of a two-atom system in an entangled state and the Fulling–Davies–Unruh effect: The electromagnetic field case

Abstract

We explore, respectively, from the viewpoints of a locally inertial observer and a coaccelerated observer, the transition rates of a two-atom system in the symmetric or antisymmetric entangled state, [Formula: see text] or [Formula: see text], and coupled to the electromagnetic fields. The interatomic separation is assumed to be constant and perpendicular to the acceleration; the fields to which the atoms are coupled are assumed to be in the vacuum state in the locally inertial frame and in a thermal state in the coaccelerated frame. We find that, in the viewpoints of the two observers, both the downward transition [Formula: see text] and the upward transition [Formula: see text] can take place, where [Formula: see text] and [Formula: see text] denote two eigenstates of the two-atom system with both atoms in their ground states and excited states, respectively. With an appropriate choice of the orientations of the atomic dipole moments, coherent radiation can happen for a system in acceleration but not for one in inertial motion. By comparing the transition rates viewed by the two observers, we show that the transition rates of the accelerated two-atom system viewed by a locally inertial observer can only be recovered in the coaccelerated frame by assuming a thermal bath at the Fulling–Davies–Unruh temperature. The effects of these collective transitions on the evolution of energy of the two-atom system are also analyzed.