Feedback-control of quantum systems using continuous state-estimation

Abstract

We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. Direct feedback may be combined with feedback by estimation, and the resulting combination, performed on a linear system, is closely analogous to classical LQG control theory with residual feedback.

12 pages, multicol revtex, revised and extended

References in corpus (9)

• Preparation of Nonclassical States in Cavities with a Moving Mirror
• Continuous quantum measurement and Itô formalism
• Optomechanical Cooling of a Macroscopic Oscillator by Homodyne Feedback
• Cooling the Collective Motion of Trapped Ions to Initialize a Quantum Register
• Full observation of single-atom dynamics in cavity QED
• Stochastic pure state representation for open quantum systems
• Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion
• Linear quantum trajectories: Applications to continuous projection measurements
• Continuous stochastic Schrodinger equations and localization

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