https://hal-mines-paristech.archives-ouvertes.fr/hal-00829864Somaraju, Ram AbhinavRam AbhinavSomarajuSISYPHE - SIgnals and SYstems in PHysiology & Engineering - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en AutomatiqueMirrahimi, MazyarMazyarMirrahimiSISYPHE - SIgnals and SYstems in PHysiology & Engineering - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en AutomatiqueRouchon, PierrePierreRouchonCAS - Centre Automatique et Systèmes - MINES ParisTech - École nationale supérieure des mines de Paris - PSL - Université Paris sciences et lettresApproximate stabilization of an infinite dimensional quantum stochastic systemHAL CCSD2013Quantum feedback controlstochastic stabilizationinfinite dimensional stochastic systems[SPI.AUTO] Engineering Sciences [physics]/AutomaticChaplais, François2013-06-04 06:30:392022-01-21 03:14:522013-06-10 09:09:18enJournal articleshttps://hal-mines-paristech.archives-ouvertes.fr/hal-00829864/document10.1142/S0129055X13500013application/pdf1We 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.