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Journal articles
Approximate stabilization of an infinite dimensional quantum stochastic system
Abstract : We study the state feedback stabilization of a quantum harmonic oscillator near a pre-specified Fock state (photon number state). Such a state feedback controller has been recently implemented on a quantized electromagnetic field in an almost lossless cavity. Such open quantum systems are governed by a controlled discrete-time Markov chain in the unit ball of an infinite dimensional Hilbert space. The control design is based on an unbounded Lyapunov function that is minimized at each time-step by feedback. This ensures (weak-*) convergence of probability measures to a final measure concentrated on the target Fock state with a pre-specified probability. This probability may be made arbitrarily close to 1 by choosing the feedback parameters and the Lyapunov function. They are chosen so that the stochastic flow that describes the Markov process may be shown to be tight (concentrated on a compact set with probability arbitrarily close to 1). Convergence proof uses Prohorov's theorem and specific properties of this Lyapunov function.
Cited literature [13 references]
https://hal-mines-paristech.archives-ouvertes.fr/hal-00829864
Contributor : François Chaplais Connect in order to contact the contributor
Submitted on : Tuesday, June 4, 2013 - 6:30:39 AM
Last modification on : Tuesday, January 11, 2022 - 11:16:23 AM
Long-term archiving on: : Thursday, September 5, 2013 - 4:20:11 AM
Contributor : François Chaplais Connect in order to contact the contributor
Submitted on : Tuesday, June 4, 2013 - 6:30:39 AM
Last modification on : Tuesday, January 11, 2022 - 11:16:23 AM
Long-term archiving on: : Thursday, September 5, 2013 - 4:20:11 AM
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StabilizationQuantum.pdf
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