Temporal interference effects in noncollinear and frequency-nondegenerate spontaneous parametric down-conversion

TL;DR

This paper investigates interference effects in noncollinear, frequency-nondegenerate spontaneous parametric down-conversion, revealing controllable photon propagation and strong quantum interference patterns influenced by nondegeneracy parameters.

Contribution

It introduces a novel analysis of interference effects in noncollinear, frequency-nondegenerate SPDC, linking nondegeneracy to observable interference phenomena and temporal comb structures.

Findings

Photon emission occurs along two cones with angles determined by nondegeneracy.

Interference patterns form finite-size temporal combs with quantum beats.

The degree of nondegeneracy controls the structure of temporal interference patterns.

Abstract

We consider regimes of Spontaneous Parametric Down-Conversion both noncollinear and nondegenerate in frequencies. Parameters characterizing degrees of noncollinearity and of nondgeneracy are defined, and they are shown to be not independent of each other. At a given degree of nondegeneracy the emitted photons are shown to propagate along two different cones opening angles of which are determined by the degree of nondegeneracy. Based on this, the degree of nondegeneracy can be controlled by means of the angular selection of photons, e.g., with the help of appropriately installed slits. For such selected photons their wave functions are found depending on two frequency or on two temporal variables. Interference effects arising in such states are tested by analyzes of the Hong-Ou-Mandel type scheme with the varying delay time in one of two channels and with photons from two channels sent to the beamsplitter. The temporal pictures arising after the beamsplitter are found to demonstrate extremely strong interference exhibiting itself in formation of finite-size temporal combs filled with quantum beats. Parameters of combs depend on the degree of nondegeneracy, and the physical reasons of this dependence are clarified.