Collective transitions of two entangled atoms and the Fulling-Davies-Unruh effect

Abstract

We calculate respectively, from the viewpoints of an instantaneously/locally inertial observer and a coaccelerated observer, the transition rates of the two-atom system in the symmetric/antisymmetric entangled state [$|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩$]. The scalar fields to which the atoms are coupled are respectively assumed to be in the vacuum state and a thermal state in the instantaneously inertial frame and in the coaccelerated frame. We show that both the upward transition $|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩\ensuremath{\rightarrow}|{e}_{A}{e}_{B}⟩$ and the downward transition $|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩\ensuremath{\rightarrow}|{g}_{A}{g}_{B}⟩$ take place, where $|{g}_{A}{g}_{B}⟩$ and $|{e}_{A}{e}_{B}⟩$ represent two collective eigenstates of the two-atom system with both atoms in their ground state and excited state respectively, and the transition rates observed in the two frames are identical only if there exists a thermal bath at the Fulling-Davies-Unruh temperature in the coaccelerated frame. Though both the downward and upward transition rates are characterized by the Plankian factor, this factor does not show up in the average variation rate of energy of the two-atom system, as a result of the perfect cancellation of the terms in the transition rates in the instantaneously inertial frame multiplied by the Plankian factor which corresponds to the Unruh thermal bath, and the cancellation of the temperature-dependent terms in the transition rates observed in the coaccelerated frame. A comparison of the transition rates of a static two-atom system in interaction with the massless scalar field in a thermal state at an arbitrary temperature with those of a uniformly accelerated two-atom system in interaction with the vacuum massless scalar field shows that the equivalence between the thermal bath and the uniform acceleration, which is well known to be valid for the single atom case, no longer holds for the two-atom system in the symmetric/antisymmetric entangled state. The effect of atomic uniform acceleration in the transition rates of the two-atom system, and the roles of both the downward and the upward transitions in the disentanglement of the two-atom system are also discussed.