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 photon is different from the same of the Rindler detector which is in interaction with a coherent Minkowski photon. Situation does not change in the response of quantum detector for the classical limit of the photon state. This we investigate in $(1+1)$ and $(3+1)$-spacetime dimensions. Interestingly, the transition probabilities of the ``classical'' detector in the classical limit of the photon state in $(1+1)$-dimensions, for these two scenarios, appear to be identical when the frequencies of photon mode and detector are taken to be same. However, our obtained detector's transition probabilities in $(3+1)$-dimensions, which are calculated under the large acceleration condition, do not show such signature. The implications of these observations are discussed as well.