Counter-propagating spontaneous four wave mixing: photon-pair factorability and ultra-narrowband single photon

TL;DR

This paper introduces a novel counter-propagating spontaneous four wave mixing process in guided-wave media, enabling automatic phase matching, factorable photon pairs, and ultra-narrowband single photons suitable for quantum interfaces.

Contribution

It presents a new CP-SFWM process with automatic phase matching and factorability, achieving ultra-narrowband photons without cavities.

Findings

Automatic phase matching regardless of dispersion.

Generation of factorable photon pairs with simple configurations.

Production of MHz bandwidth photons compatible with atomic transitions.

Abstract

We introduce a new kind of spontaneous four wave mixing process for the generation of photon pairs, in which the four waves involved counter-propagate in a guided-wave \chi^{(3)} medium; we refer to this process as counter-propagating spontaneous four wave mixing (CP-SFWM). We show that for the simplest CP-SFWM source, in which all waves propagate in the same polarization and transverse mode and in which self- and cross-phase modulation effects are negligible, phasematching is attained automatically regardless of dispersion in the fiber or waveguide. Furthermore, we show that in two distinct versions of this source (both pumps pulsed, or one pump pulsed and the remaining one monochromatic), the two-photon state is automatically factorable provided that the length of the nonlinear medium exceeds a certain threshold, easily achievable in practice since this threshold length tends to be in the range of mm to cm. We also show that if one of the pumps approaches the monochromatic limit, and for a sufficient nonlinear medium length, the bandwidth of one of the two photons in a given pair may be reduced to the level of MHz, compatible with electronic transitions for the implementation of atom-photon interfaces, without the use of optical cavities.