A general framework for multimode Gaussian quantum optics and photo-detection: application to Hong-Ou-Mandel interference with filtered heralded single photon sources

TL;DR

This paper develops a comprehensive theoretical framework for multimode Gaussian quantum optics and photo-detection, analyzing how spectral and photon number impurities affect Hong-Ou-Mandel interference visibility in heralded single photon sources.

Contribution

It introduces a general model incorporating multiple spatial and spectral modes, linear and nonlinear elements, and detection types to study interference effects in quantum optics.

Findings

Increasing photon generation rate reduces interference visibility.

Spectral filtering improves purity but decreases heralding efficiency at higher powers.

Maximum generation rate is limited by spectral impurity effects.

Abstract

The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involves maximising the interference visibility whilst maintaining an acceptable photon generation rate. By developing a general theoretical framework that allows us to include large numbers of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong--Ou--Mandel interference visibility of parametric photon sources, considering both threshold and number resolving detectors, together with the effects of spectral filtering. We find that for any degree of spectral impurity, increasing the photon generation rate necessarily decreases the interference visibility, even when using number resolving detection. While tight spectral filtering can be used to enforce spectral purity and increased interference visibility at low powers, we find that the induced photon number impurity results in a decreasing interference visibility and heralding efficiency with pump power, while the maximum generation rate is also reduced.