@inproceedings{a4d4b0dec44747bda8a011949009b60f,
title = "Approximate stabilization of an infinite dimensional quantum stochastic system",
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.",
author = "Ram Somaraju and Mazyar Mirrahimi and Pierre Rouchon",
year = "2011",
month = jan,
day = "1",
doi = "10.1109/CDC.2011.6160560",
language = "English",
isbn = "9781612848006",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "6248--6253",
booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",
note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",
}