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Proceedings of the ... American Control Conference/Proceedings of the American Control Conference

A time-varying Kalman filter approach to integral LQG frequency locking of an optical cavity

S. Z. Sayed Hassen, Ian R. Petersen

Published Jun 1, 2010• 8 citations
Publisher

Abstract

In this paper, we address the problem of frequency locking an optical cavity which arises in the field of quantum optics. The cavity frequency locking problem involves matching the resonant frequency of an optical cavity to that of an incoming laser beam. We model the measurement nonlinearity inherent in the optical cavity and place instantaneous bounds on the observation errors. A convex set within which the error between the laser frequency and the cavity resonant frequency lies is determined and we synthesize a time-varying integral LQG controller which uses information from this set. Simulation results are shown to validate our design in the nonlinear region of operation.

DOI
10.1109/acc.2010.5531631

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Proceedings of the ... American Control Conference/Proceedings of the American Control Conference•Jun 1, 2010•16 citations
In this paper, we address the problem of frequency locking an optical cavity which arises in the field of quantum optics. The cavity frequency locking problem involves matching the resonant frequency of an optical cavity to that of an incoming laser beam. We model the measurement nonlinearity inherent in the optical cavity and place instantaneous bounds on the observation errors. A convex set within which the error between the laser frequency and the cavity resonant frequency lies is determined and we synthesize a time-varying integral LQG controller which uses information from this set. Simulation results are shown to validate our design in the nonlinear region of operation.
The cavity frequency locking problem, which arises in the field of quantum optics, involves matching the resonant frequency of an optical cavity to that of an incoming laser. Although this problem is investigated using linear control techniques for small perturbations, in this brief, we address the nonlinear control problem of frequency locking an optical cavity. Models of the measurement nonlinearities inherent in optical cavities are derived using a singular perturbation approach and instantaneous bounds are placed on the observation errors. A convex set within which the error between the laser frequency and the cavity resonant frequency lies is then determined at each time step by solving two high-order polynomial equations. Based on a reduced-order model of the cavity, a time-varying Kalman filter is designed and simulation results are presented to validate our controller on a full-model of the cavity in the nonlinear region of operation.
This paper considers the application of Linear Quadratic Gaussian (LQG) optimal control theory to a problem of cavity locking in quantum optics. Using an equivalence between quantum LQG control and classical LQG control, this problem is reduced to a standard LQG control problem. The cavity locking problem involves controlling the error between the laser frequency and the cavity frequency. A model for the cavity system is set up and an LQG controller is synthesized. The resulting control system implemented on an experimental cavity.
Systematic approaches to the design of quantum optical systems will become more and more important as their complexity grows. One such systematic technique is the Linear Quadratic Gaussian (LQG) methodology. Here we describe the design and implementation of a LQG feedback controller in a quantum optical experiment—frequency‐locking an optical cavity to a laser. The successful implementation of the LQG design procedure to this particular problem lays the groundwork for the application of other modern control techniques to quantum optical systems. Our results are promising for future, more complex stabilisation problems in quantum optics, as the described approach is inherently multi‐variable and naturally incorporates multiple sensors and actuators as well as nested loops.
We show that a systematic modern control technique such as linear–quadratic Gaussian (LQG) control can be applied to a problem in experimental quantum optics which has previously been addressed using traditional approaches to controller design. An LQG controller which includes integral action is synthesized to stabilize the frequency of the cavity to the laser frequency and to reject low frequency noise. The controller is successfully implemented in the laboratory using a dSpace digital signal processing board. One important advantage of the LQG technique is that it can be extended in a straightforward way to control systems with multiple measurements and multiple feedback loops. This work is expected to pave the way for extremely stable lasers with fluctuations approaching the quantum noise limit and which could be potentially used in a wide range of applications.
In this paper, we consider the application of linear quadratic Gaussian (LQG) control to the problem of optimizing the level of squeezing in one of the quadratures of an optical field. Squeezed states of light can be generated when two optical fields (at fundamental and second-harmonic frequencies) interact in an optical cavity in the presence of a second-order nonlinear crystal. Our system is an optical squeezer which is modelled as a nonlinear quantum system. Suitable models for the quantum and classical noises present in the system are used and laser phase noise which arises due to mechanical vibration of the mirror(s) in the beam path is modeled as (approximately) integrated white noise. An LQG controller is synthesized and the closed loop system is simulated to validate our design.