Detector's response to coherent Rindler and Minkowski photons

We observe that the transition probability in a static two-level quantum detector interacting with a coherent Rindler field mode differs from that of the Rindler detector interacting with a coherent Minkowski field mode. The situation does not change in the quantum detector's response in the semiclassical limit of the field state. This we investigate in $(1+1)$ and $(3+1)$-spacetime dimensions. Interestingly, in $(1+1)$-dimensions, the transition probabilities of the ``classical'' detector in the semiclassical limit of the field state for these two scenarios appear to be identical when the field mode and detector frequencies are taken to be the same. However, in $(3+1)$ dimensions, the detector transition probabilities calculated under the large-acceleration condition do not exhibit such a signature. The implications of these observations are also discussed.