Semiclassical Wigner distribution for two-mode entangled state

TL;DR

This paper derives a steady-state solution for the nondegenerate optical parametric oscillator's Wigner distribution, revealing the intracavity two-mode entangled state across all regimes, including non-Gaussian above threshold states.

Contribution

It introduces a heuristic method to obtain the steady-state Wigner distribution for a nondegenerate optical parametric oscillator with adiabatic pump elimination, capturing non-Gaussian features.

Findings

Provides a steady-state Wigner distribution valid in all regimes.

Reveals non-Gaussian distribution above threshold.

Offers insights into intracavity two-mode entanglement.

Abstract

We derive the steady state solution of the Fokker-Planck equation that describes the dynamics of the nondegenerate optical parametric oscillator in the truncated Wigner representation of the density operator. We assume that the pump mode is strongly damped, which permits its adiabatic elimination. When the elimination is correctly executed, the resulting stochastic equations contain multiplicative noise terms, and do not admit a potential solution. However, we develop an heuristic scheme leading to a satisfactory steady-state solution. This provides a clear view of the intracavity two-mode entangled state valid in all operating regimes of the OPO. A nongaussian distribution is obtained for the above threshold solution.