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 mirror is static in Minkowski spacetime while the atom is attached to a frame confined inside the future or past light cone region, ( ii ) an atom is static in Minkowski spacetime, and the mirror is confined inside the future or past light cone region. For both situations the atom is interacting with field modes defined in mirror's frame. Analogous configurations are considered in the black hole spacetime: in one case, the mirror carries field modes represented by the Kruskal time, while the atom follows the Schwarzschild time defined inside the black hole; in the other case, the situations are reversed. The analyses, 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 depend periodically on the separation between the atom and the mirror. At the level of transition probabilities, the aforesaid two scenarios in (1+1) dimensional Minkowski-light cone regions appear to be the same for the equal 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 excitation to de-excitation ratios (EDRs) corresponding to analogous scenarios are equal for equal atomic and field frequencies. This bolsters our earlier observation on the relevance of EDRs [1] in the context of the quantum equivalence between analogous scenarios.