Quantum Popov robust stability analysis of an optical cavity containing a saturated Kerr medium

TL;DR

This paper develops a quantum Popov stability criterion for analyzing the robust stability of an optical cavity with a saturated Kerr medium, extending quantum control methods to nonlinear quantum optical systems.

Contribution

It introduces a quantum Popov stability criterion for nonlinear quantum systems with sector bounded nonlinearities, specifically applied to an optical cavity with a saturated Kerr medium.

Findings

Quantum small gain theorem applied to the system.

Development of a non-quadratic quantum Popov stability criterion.

Successful stability analysis of the optical cavity system.

Abstract

This paper applies results on the robust stability of nonlinear quantum systems to a system consisting an optical cavity containing a saturated Kerr medium. The system is characterized by a Hamiltonian operator which contains a non-quadratic term involving a quartic function of the annihilation and creation operators. A saturated version of the Kerr nonlinearity leads to a sector bounded nonlinearity which enables a quantum small gain theorem to be applied to this system in order to analyze its stability. Also, a non-quadratic version of a quantum Popov stability criterion is presented and applied to analyze the stability of this system.