Interference of N photons with detection capable of precise resolution of time of arrival
In this work, we develop the distinguishing theory of N single photons for the interference with photon detection capable of accurate resolution of time of arrival (detectors faster than photon duration). We demonstrate the appearance of partial distinguishability of N photons in interference experiments with detection with precise time resolution due to mixed states of photons, i.e., uncertainties in photon parameters. Detailed analysis is carried out using the Gaussian photons model with time of arrival distributed according to a Gaussian as well (which allows exact results). We show that the distribution of probabilities at the output of a spatial interferometer has the same form as in the case of detection without resolution of arrival time, where a function of the group of permutations of N objects serves as distinguishabiliyt function. We reproduce the previously published results on the subject, where photons were supposed to be in pure states, but we go beyond them, in particular, we find that photon distinguishability due to mixed states cannot be compensated for by any detection even that with absolute precision.