Quantum correlation in degenerate optical parametric oscillators with mutual injections

TL;DR

This paper investigates the quantum dynamics of two mutually injected degenerate optical parametric oscillators, revealing quantum correlations, entanglement, and macroscopic superpositions influenced by system losses and the injection path.

Contribution

It provides a theoretical and numerical analysis of quantum correlations and superpositions in coupled OPOs considering the cavity mode explicitly, advancing understanding of quantum effects in such systems.

Findings

Positive quantum correlation near the oscillation threshold

Entanglement between intracavity fields

Macroscopic superpositions form at phase transition with low loss

Abstract

We theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive $P$ representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections is simulated, and its quantum state is investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadratic amplitudes $\hat{p}$ in the oscillators are positively correlated near the oscillation threshold. It indicates finite quantum correlation, estimated via Gaussian quantum discord, and the entanglement between the intracavity subharmonic fields. When the loss in the injection path is low, each oscillator around the phase transition point forms macroscopic superposition even under a small pump noise. It suggests that the squeezed field stored in the low-loss injection path weakens the decoherence in the oscillators.