Two-path interference of single-particle pulses measured by the Unruh-DeWitt-type quantum detector

We study the two-path interference of single-particle pulses measured by the Unruh-DeWitt-type quantum detector, which itself is a quantum state as well as the incoming pulse, and of which the interaction with the pulse is described by unitary quantum evolution instead of a nonunitary collapsing process. Provided that the quantum detector remains coherent in time long enough, the detection probability still manifests the two-path interference pattern even if the length difference between the two paths considerably exceeds the coherence length of the single-particle pulse, contrary to the result measured by an ordinary classical detector. Furthermore, it is formally shown that an ensemble of identical Unruh-DeWitt-type quantum detectors collectively behaves as an ordinary classical detector, if coherence in time of each individual quantum detector becomes sufficiently short. Our study provides a concrete yet manageable theoretical model to investigate the two-path interference measured by a quantum detector and facilitates a quantitative analysis of the difference between classical and quantum detectors. The analysis affirms the main idea of decoherence theory: quantum behavior is lost as a result of quantum decoherence.Comment: 20 pages, 2 figures; v4: various revisions made, version to appear in J. Phys. A: Math. Theo