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AIP conference proceedings

Laser Frequency Locking to an Optical Cavity using LQG Control

M. Heurs, Elanor H. Huntington, S. Z. Sayed Hassen, Idar Petersen, M. R. James, Alexander I. Lvovsky

Published Jan 1, 2009• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.3131331

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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.
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.
This paper describes a new optical cavity controller test bed system for implementing modern quantum control techniques, with an emphasis on the control of optical cavities. One such quantum control task is the frequency locking of an optical cavity. Locking an optical cavity refers to the process of matching the input laser frequency to the cavity's resonant frequency. Any deviation in the two frequencies, characterized in terms of the detuning, is undesirable. The test bed comprises an input laser, a three-mirror ring cavity, the associated optics, and a dSPACE digital signal processing system. The detuning in the system is measured in the form of an error signal, which is fed to a controller. The controller provides a suitable control input to a piezoelectric actuator mounted on one of the mirrors, altering the resonant frequency of the cavity to achieve zero detuning. The dynamics of the cavity and the piezoelectric actuator are modeled using system identification methods, an integral linear quadratic Gaussian controller is designed and implemented in dSPACE, and experimental results are presented.
Quantum control theory is a rapidly evolving research field, which has developed over the last three decades. Quantum optics has practical importance in quantum technology and provides a promising means of implementing quantum information and computing device. \nIn quantum control, it is difficult to acquire information about quantum states without destroying them since microscopic quantum systems have many unique characteristics such as entanglement and coherence which do not occur in classical mechanical system. Therefore, \nthe Lyapunov-based control methodology is used to first construct an artificial closed-loop controller and then an open-loop law is derived by simulation of the artificial closed-loop system. \n \nThis work considers the stabilization of laser cavity as the main integral part of quantum optical systems through squeezing the output beam of the cavity. As a comprehensive example of this type of system, quantum optomechanical sensors are investigated. To this end, a nonlinear model \nof quantum optomechanical sensors is first extended incorporating various noises. Then, linear quadratic Gaussian (LQG) control method is used to tackle the problem of mode-squeezing in optomechanical sensors. \nCoherent feedback quantum control is synthesized by incorporating both shot noise and back-action noise to attenuate the output noise well below the shot noise level (Two waves are said to be coherent if they have a constant relative phase). In the second phase of this work, due to entanglement of the system with critical uncertainties and technical limitations such as laser noise and detector imprecision, robust H [infinity] method is employed for the robust stabilization and robust performance of the system in practice. In H [infinity] methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this. The effectiveness of the proposed control strategy in squeezing the cavity output beam is demonstrated by simulation.
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.