Stabilization of photon-number states via single-photon corrections: a first convergence analysis under an ideal set-up

H.B. Silveira 1 Paulo Sergio Pereira da Silva 2 Pierre Rouchon 3, 4
1 DAS - Department of Automation and Systems
2 Escola Politecnica
3 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, MINES ParisTech - École nationale supérieure des mines de Paris, CNRS - Centre National de la Recherche Scientifique : UMR8551
4 CAS - Centre Automatique et Systèmes
Abstract : This paper presents a first mathematical convergence analysis of a Fock states feedback stabilization scheme via single-photon corrections. This measurement-based feedback has been developed and experimentally tested in 2012 by the cavity quantum electrodynamics group of Serge Haroche and Jean-Michel Raimond. Here, we consider the infinite-dimensional Markov model corresponding to the ideal setup where detection errors and feedback delays have been disregarded. In this ideal context, we show that any goal Fock state can be stabilized by a Lyapunov-based feedback for any initial quantum state belonging to the dense subset of finite rank density operators with support in a finite photon-number sub-space. Closed-loop simulations illustrate the performance of the feedback law.
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H.B. Silveira, Paulo Sergio Pereira da Silva, Pierre Rouchon. Stabilization of photon-number states via single-photon corrections: a first convergence analysis under an ideal set-up. 54th IEEE Conference on Decision and Control (CDC 2015), Dec 2015, Osaka, Japan. ⟨hal-01245104⟩

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