Timelike transitions in an atom by a mirror in light cone and Kruskal-Szekeres regions: a status of quantum equivalence

Abstract: We investigate the timelike transitions in a two-level atom in the presence of an infinite reflecting mirror in the future-past light cone regions of a Minkowski spacetime as well as in the region interior of a $(1+1)$ dimensional Schwarzschild black hole. In particular, when considering the light cone regions, two specific scenarios are dealt with -- $(i)$ a static mirror is synchronized with Minkowski time while the static atom is using a frame in the light cone, $(ii)$ a static atom is using Minkowski time, and the mirror is using the light cone frame. Analogous scenarios in the black hole spacetime are -- the static mirror uses future Kruskal frame while the static atom uses the Schwarzschild coordinates, defined inside the black hole, and vice-versa. The calculations, depending upon the frame of the atom, are respectively done within the light cone, Minkowski, Schwarzschild, and Kruskal time-interaction pictures. In all of these scenarios, we observe that the excitation probabilities contain a thermal factor and are periodic on the separation between the atom and the mirror, contrasting the uniform acceleration scenario. The above two scenarios in $(1+1)$ dimensional Minkowski-light cone regions appear to be the same when we equate the field and atomic frequencies. However, the same is not true when we consider the $(3+1)$ dimensional Minkowski-light cone or the Schwarzschild interior regions. We also estimate the de-excitation probabilities and encounter similar situations. However, we observe that the ratio between the excitation and corresponding de-excitation probabilities resembles the classical equivalence in motion at the quantum level. The excitation to de-excitation ratios (EDRs) corresponding to analogous scenarios are equal for equal atomic and field frequencies. This bolsters our earlier proposal on the relevance of EDRs in the context of the equivalence principle.