Approximate stabilization of an infinite dimensional quantum stochastic system - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Reviews in Mathematical Physics Année : 2013

Approximate stabilization of an infinite dimensional quantum stochastic system

(1) , (1) , (2)
1
2

Résumé

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.
Fichier principal
Vignette du fichier
StabilizationQuantum.pdf (235.22 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00829864 , version 1 (04-06-2013)

Identifiants

Citer

Ram Abhinav Somaraju, Mazyar Mirrahimi, Pierre Rouchon. Approximate stabilization of an infinite dimensional quantum stochastic system. Reviews in Mathematical Physics, 2013, 25 (1), pp.1350001. ⟨10.1142/S0129055X13500013⟩. ⟨hal-00829864⟩
225 Consultations
157 Téléchargements

Altmetric

Partager

Gmail Facebook Twitter LinkedIn More