Hong-Ou-Mandel effect in terms of the temporal biphoton wave function with two arrival-time variables

TL;DR

This paper analyzes the Hong-Ou-Mandel effect using biphoton wave functions dependent on two frequency and two time variables, clarifying conditions under which the effect diminishes or disappears.

Contribution

It introduces explicit expressions for probability densities based on biphoton temporal and frequency wave functions, enhancing understanding of the effect's dependence on photon properties.

Findings

Identifies conditions reducing the Hong-Ou-Mandel effect

Provides explicit formulas for photon split and unsplit probabilities

Clarifies the role of photon delay and polarization in the effect

Abstract

The well-known Hong-Ou-Mandel effect is revisited. Two physical reasons are discussed for the effect to be less pronounced or even to disappear: differing polarizations of photons coming to the beamsplitter and delay time of photons in one of two channels. For the latter we use the concepts of biphoton frequency and temporal wave functions depending, correspondingly, on two frequency continuous variables of photons and on two time variables $t_1$ and $t_2$ interpreted as the arrival times of photons to the beamsplitter. Explicit expressions are found for the probability densities and total probabilities for photon pairs to be split between two channels after the beamsplitter and to be unsplit, when two photons appear together in one of two channels.