Approximate stabilization of an infinite dimensional quantum stochastic system

Ram Somaraju (1) , Mazyar Mirrahimi (1) , Pierre Rouchon (2)

1 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
2 CAS - Centre Automatique et Systèmes

We propose a feedback scheme for preparation of photon number states in a microwave cavity. Quantum Non-Demolition (QND) measurements of the cavity field and a control signal consisting of a microwave pulse injected into the cavity are used to drive the system towards a desired target photon number state. Unlike previous work, we do not use the Galerkin approximation of truncating the infinite-dimensional system Hilbert space into a finite-dimensional subspace. We use an (unbounded) strict Lyapunov function and prove that a feedback scheme that minimizes the expectation value of the Lyapunov function at each time step stabilizes the system at the desired photon number state with (a pre-specified) arbitrarily high probability. Simulations of this scheme demonstrate that we improve the performance of the controller by reducing "leakage" to high photon numbers.

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Ram Somaraju, Mazyar Mirrahimi, Pierre Rouchon. Approximate stabilization of an infinite dimensional quantum stochastic system. CDC-ECC 2011 : 50th IEEE Conference on Decision and Control and European Control Conference, Dec 2011, Orlando, United States. pp.6248 - 6253, ⟨10.1109/CDC.2011.6160560⟩. ⟨hal-00683444⟩