Equivalence in virtual transitions between uniformly accelerated and static atoms: from a bird's eye

We study the prospect of the equivalence principle at the quantum regime by investigating the transition probabilities of a two-level atomic detector in different scenarios. In particular, two specific set-ups are considered. ($i$) $Without~a~boundary$: In one scenario the atom is in uniform acceleration and interacting with Minkowski field modes. While in the other the atom is static and in interaction with Rindler field modes. ($ii$) $With~a~reflecting~boundary$: In one scenario, the atom is uniformly accelerated, and the mirror is static, and in the other scenario, the atom is static, and the mirror is in uniform acceleration. In these cases, the atom interacts with the field modes, defined in the mirror's frame. For both the set-ups, the focus is on the excitation and de-excitation probabilities in $(1+1)$ and $(3+1)$ spacetime dimensions. Our observations affirm that in $(1+1)$ dimensions, for both set-ups the transition probabilities from different scenarios become the same when the atomic and the field frequencies are equal. In contrast, in $(3+1)$ dimensions this equivalence is not observed in general, inspiring us to look for a deeper physical interpretation. Our findings suggest that when the equivalence between different scenarios is concerned, the excitation to de-excitation ratio provides a more consistent measure even in $(3+1)$ dimensions. We discuss the physical interpretation and implications of our findings.