On Selecting Optimal Parameters for Delay Time Measurement Using the Hong–Ou–Mandel Effect

The paper deals with the measurement error of the delay time between the arrivals at the beam splitter of two photons traveling through different channels in an optical system based on a Hong-Ou-Mandel (HOM) interferometer. We consider the source of two-photon light to be the radiation of spontaneous parametric scattering (SPS) of light of the second type. The photon delay in one of the HOM interferometer channels can be induced by a change in the optical path length due to various factors: mechanical displacement of interferometer parts, changes in the refractive index of the medium caused by temperature variations, electric fields, etc. In the scheme, the outputs of the beam splitter are connected to single-photon detectors, which send signals to a coincidence counter upon photon detection. The coincidence counter data determine the delay time. The authors determine the absolute error in estimating the delay time in terms of the biphoton spectral width, the visibility, calculated from the maximum and minimum values of the coincidence counter signal, and the estimated delay time value itself. The derived expression facilitates finding the estimated delay time value. The study reveals that for a fixed biphoton field width, the delay time corresponding to the minimum absolute error value approaches the inflection point of the coincidence-time curve with decreasing visibility. This should be taken into account when designing measuring devices based on the Hong-Ou-Mandel interferometer.