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arXiv:1304.5384 · Quantum Science and Technology

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

Ian R. Petersen

Published Jul 1, 2013• 16 citations
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Abstract

Abstract This paper applies results of the robust stability of nonlinear quantum systems to a system consisting of an optical cavity containing a saturated Kerr medium. The system is characterised by a Hamiltonian operator that 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 that enables a quantum small gain theorem to be applied to this system in order to analyse its stability. Also, a non-quadratic version of a quantum Popov stability criterion is presented and applied to analyse the stability of this system.

DOI
10.1088/2058-9565/aa77d2

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Abstract This paper applies results of the robust stability of nonlinear quantum systems to a system consisting of an optical cavity containing a saturated Kerr medium. The system is characterised by a Hamiltonian operator that 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 that enables a quantum small gain theorem to be applied to this system in order to analyse its stability. Also, a non-quadratic version of a quantum Popov stability criterion is presented and applied to analyse the stability of this system.
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic perturbations to the system Hamiltonian. The paper extends recent results on the robust stability of nonlinear quantum systems to allow for non-quadratic perturbations to the Hamiltonian which depend on multiple parameters. A robust stability condition is given in terms of a strict bounded real condition. This result is then applied to the robust stability analysis of a nonlinear quantum system which is a model of an optical parametric amplifier.
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of coupling operators and a quadratic Hamiltonian. This paper extends previous results on the robust stability of nonlinear quantum systems to allow for quantum systems with dynamic uncertainties. These dynamic uncertainties are required to satisfy a certain quantum stochastic integral quadratic constraint. The robust stability condition is given in terms of a strict bounded real condition. This result is applied to the robust stability analysis of an optical parametric amplifier.
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