Comprehensive interference characteristics of a three-parameter Hong–Ou–Mandel interferometer

We theoretically extend the original Hong–Ou–Mandel (HOM) interferometer to three parameters by concatenating 50:50 beam splitters with three independent and adjustable time delays. The coincidence probability of such an interferometer is obtained based on the linear transformation of the beam splitter matrix. We present a comprehensive analysis of the interference characteristics of the interferometer at different time delays with various types of frequency-correlated resources and input states. It is found that by properly setting the time delays, one can obtain typical interferograms that include multiple sub-interferograms associated with one- and two-parameter HOM interferometers, revealing richer and more complicated two-photon interference phenomena. In particular, additional enhancements of the interference signal at a specific delay can be achieved, and the symmetry of the interferograms on both sides can also be changed. This work provides comprehensive insights into the interference characteristics of the three-parameter HOM interferometer and enables the simultaneous optimal estimation of multiple time-delay parameters within a single interferometer, which holds potential for applications in multiparameter estimation and quantum metrology.