Quantum state of an injected TROPO above threshold : purity, Glauber function and photon number distribution

TL;DR

This paper analyzes the quantum properties of a triply resonant optical parametric oscillator above threshold with injected signals, focusing on spectral purity, Glauber function, and photon distribution, revealing dependencies on injection strength and asymmetry.

Contribution

It provides a detailed quantum state characterization of the OPO above threshold with injection, including purity and photon distribution, which was not previously fully explored.

Findings

Spectral purity depends on injection intensity and asymmetry.

Derived the three-mode Glauber P-function for the system.

Calculated the joint photon number distribution and its dependence on injection.

Abstract

In this paper we investigate several properties of the full signal-idler-pump mode quantum state generated by a triply resonant non-degenerate Optical Parametric Oscillator operating above threshold, with an injected wave on the signal and idler modes in order to lock the phase diffusion process. We determine and discuss the spectral purity of this state, which turns out not to be always equal to 1 even though the three interacting modes have been taken into account at the quantum level. We have seen that the purity is essentially dependent on the weak intensity of the injected light and on an asymmetry of the synchronization. We then derive the expression of its total three-mode Glauber P-function, and calculate the joint signal-idler photon number probability distribution and investigate their dependence on the injection.