LQG control of an optical squeezer

2013 9th Asian Control Conference (ASCC)

2013

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.

Section: Robust Stability Analysis Of An Optical Parametric Amplmentioning

confidence: 92%

Section: Robust Stability Analysis Of An Optical Parametric Amplmentioning

confidence: 99%

Robust stability analysis of an optical parametric amplifier quantum system

2013 9th Asian Control Conference (ASCC)

2013

“…Hence, we do not wish to significantly attenuate the effect of v 1 ( t ) on z 1 ( t ). The dynamics of the optical squeezer system can be described as in and for the chosen values of the squeezer parameters leads to a model of the form below where

\begin{matrix} A_{p} & = ([], \begin{matrix} - 13.7 & 0 & 0.2 & 0 \\ 0 & - 15.3 & 0 & 0.2 \\ - 0.2 & 0 & - 1450 & 0 \\ 0 & - 0.2 & 0 & - 1450 \end{matrix}); B_{p} = ([], \begin{matrix} 0 \\ 0 \\ 0 \\ 30.8221 \end{matrix}); D_{p} = ([], \begin{matrix} 3.0822 \\ 0 \\ 0 \\ 0 \end{matrix}); \\ K_{p} & = ([], \begin{matrix} 4.3589 & 0 & 0 & 3.1623 & 0 & 0 & 0 \\ 0 & 4.3589 & 0 & 0 & 3.1623 & 0 & 0 \\ 0 & 0 & 43.5890 & 0 & 0 & 31.6228 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 31.6228 \end{matrix}); \\ C_{p} & = ([], \begin{matrix} 13.4350 & 0 & 0 & 0 \end{matrix}); N_{p} = - 1 0^{- 6}; L_{p} = ([], \begin{matrix} - 1 & 0 & 0 & 0 & 0 & 0 & 0 \end{matrix}); \end{matrix}

H_{p} = [\begin{matrix} 44.8336 & 0 & 0 \end{matrix}]

…”

Section: Numerical Examplementioning

confidence: 99%

“…Hence, we do not wish to significantly attenuate the effect of v 1 .t / on´1.t /. The dynamics of the optical squeezer system can be described as in [17] and for the chosen values of the squeezer parameters leads to a model of the form below where We combine the squeezer system plant with an anti-aliasing filter with transfer function F .s/ D 10 sC137 to form a system of the form (1), and we sample the output of the resulting system at a sampling frequency of 2 KHz. A controller of the form (3) is designed by solving the Riccati Equations (20)-(22) for the case of one hundred samples in the interval OE0; 0:1 occurring at evenly spaced times t k .…”

Section: Numerical Examplementioning

confidence: 99%

Finite horizon H^∞ control for a class of sampled‐data linear quantum systems

Maalouf

Intl J Robust & Nonlinear

2016

“…[22]- [27]. Such an OPA can be made using a nonlinear optical medium in an optical cavity; for example, see [23], [25]- [27]. This allows for the interaction between a fundamental optical field and a second harmonic optical field.…”

Section: Irpetersen@gmailcommentioning

confidence: 99%

Robust stability of quantum systems with nonlinear dynamic uncertainties

52nd IEEE Conference on Decision and Control

2013

Abstract-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. I. INTRODUCTIONIn recent years, a number of papers have considered the feedback control of systems whose dynamics are governed by the laws of quantum mechanics instead of classical mechanics; see e.g., [17] to allow for uncertainty in the coupling operator L. Also, the results of [15] have been used in the robust stability analysis of a quantum system consisting of a Josephson junction in a resonant cavity; see [18].