Effects of a thermal bath and the accelerated motion on collective transitions of two atoms in an entangled state

Abstract

Abstract Transition rates of a uniformly accelerated atom coupled to a vacuum scalar field are identical with those of one being static in a thermal bath at a temperature proportional to the proper acceleration a, i.e., $$T_U=\frac{a}{2\pi }$$ T U = a 2 π . We discuss in this paper whether there exists such an equivalence in the electromagnetic field case if more atoms are involved. To be specific, we explore the similarities and distinctions between effects of a thermal bath and those of the uniformly accelerated motion by comparing the transition rates of a two-atom system initially in the symmetric or antisymmetric entangled state [ $$|\psi _{\pm }\rangle $$ | ψ ± ⟩ ] in two cases, i.e., two static atoms in a thermal bath [the thermal case] and two atoms uniformly accelerated in vacuum [the acceleration case]. We discover that, for some particular orientations of atomic dipole moments, coherent radiation which happens in the acceleration case never occurs in the thermal case. The rates in the acceleration case with a low acceleration which means a low $$T_U$$ T U can be smaller or larger and even equal to their counterparts in the thermal case; while the rates in the acceleration case with a high acceleration which means a high $$T_U$$ T U are always much larger than their counterparts in the thermal case. Our results suggest that effects of a thermal bath and those of the uniformly accelerated motion on transition properties of a two-atom system in $$|\psi _{\pm }\rangle $$ | ψ ± ⟩ are not necessarily distinctive, but can be equivalent if the acceleration is relatively low, depending on the value of the interatomic separation.