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arXiv · 1103.1724

Approximate stabilization of an infinite dimensional quantum stochastic system

Ram Somaraju·Mazyar Mirrahimi·Pierre Rouchon
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Abstract

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.

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Ram Somaraju, Mazyar Mirrahimi, Pierre Rouchon. 2011-03-09. Approximate stabilization of an infinite dimensional quantum stochastic system. https://arxiv.org/abs/1103.1724

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