Theory of temporal three-photon interference

TL;DR

This paper develops a theoretical framework for three-photon interference, revealing that it depends on three key parameters and enabling the exploration of complex quantum correlations in three-particle entangled states.

Contribution

It introduces a new formulation of three-photon interference based on self-interference, characterizing it with only three independent parameters, unlike the single parameter in two-photon cases.

Findings

Interference characterized by three parameters, including path-length difference and path-asymmetry.

Broader class of nonclassical three-photon effects, such as HOM-type effects.

Provides theoretical foundation for future three-photon interference experiments.

Abstract

The recent demonstrations of cascaded PDC (CPDC) and the hopeful prospects of realizing third-order PDC (TOPDC) for the generation of three-photon entangled states are paving the way for experimental studies on genuine three-photon interference. In this article, we formulate three-photon interference in terms of ``each three-photon interfering only with itself.'' We show that although a generalized two-alternative three-photon interference setup based on CPDC or TOPDC involves eight different length parameters, the interference can be fully characterized in terms of only three independent parameters. The first parameter is the three-photon path-length difference, which has a direct analog in the one-photon and two-photon cases, and the other two parameters quantify the path-asymmetry length. Unlike two-photon interference, which requires only one parameter to quantify path-asymmetry, two independent parameters are needed in three-photon interference. This results in a broader class of nonclassical three-photon effects, including three-photon HOM-type effects. Our work provides the theoretical basis for existing and future three-photon interference experiments exploring the rich and complex quantum correlations associated with three-particle entanglement and potentially enabling the development of novel protocols for harnessing those correlations.