Self-Consistent Projection Operator Theory in Nonlinear Quantum Optical Systems: A case study on Degenerate Optical Parametric Oscillators

TL;DR

This paper demonstrates that the self-consistent projection operator theory effectively analyzes nonlinear quantum optical systems, specifically degenerate optical parametric oscillators, providing accurate quantum states and improved Gaussian approximations over traditional methods.

Contribution

The paper applies a new self-consistent projection operator approach to quantum optical systems, offering a more accurate and efficient way to analyze their quantum states and dynamics.

Findings

Accurately computes quantum states at critical points.

Outperforms traditional Gaussian methods.

Efficiently describes both stationary and dynamic regimes.

Abstract

Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.