Interference of two photons of different color

TL;DR

This paper explores how two photons of different colors can interfere in a Hong-Ou-Mandel setup using active beam splitters, revealing conditions for perfect destructive interference based on their spectral properties.

Contribution

It introduces the concept of active beam splitters that enable interference of different-colored photons and analyzes specific models including a moving mirror and four-wave mixing.

Findings

Interference of different-colored photons depends on spectral relations.

Active beam splitters can induce interference not possible with passive ones.

Conditions for perfect destructive interference are derived for specific active beam splitter models.

Abstract

We consider the interference of two photons with different colors in the context of a Hong-Ou-Mandel experiment, in which single photons enter each of the input ports of a beam splitter, and exit in the same, albeit undetermined, output port. Such interference is possible if one uses an active (energy-non-conserving) beam splitter. We find scenarios in which one "red" and one "blue" photon enter the beam splitter, and either two red or two blue photons exit, but never one of each color. We show how the precise form of the active beam-splitter transformation determines in what way the spectral degrees of freedom of the input photons should be related to each other for perfect destructive interference of the different-color components in the output. We discuss two examples of active beam splitters: one is a gedanken experiment involving a moving mirror and the other is a more realistic example involving four-wave mixing in an optical fiber.