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Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics #
 

Summary: Almost Global Stochastic Feedback Stabilization
of Conditional Quantum Dynamics #
Claudio Altafini + Francesco Ticozzi #
October 28, 2005
Abstract
We propose several parametrization­free solutions to the problem of
quantum state reduction control by means of continuous measurement
and smooth quantum feedback. In particular, we design a feedback law
for which almost global stochastic feedback stabilization can be proved
analytically by means of Lyapunov techinques. This synthesis arises very
naturally from the physics of the problem, as it relies on the variance
associated with the quantum filtering process.
Keywords: Quantum Feedback, Stochastic Stabilization, Nonlinear Stochas­
tic Matrix Di#erential Equations, Quantum Filtering.
1 Introduction
Experimental techniques in quantum optics permit nowadays to continuously
monitor and modify the dynamics of a cloud of cold atoms confined in an optical
cavity [15]. The knowledge of the system state can be described by a condi­
tional dynamical equation, the so­called Stochastic Master Equation (SME),
obtained from a suitable quantum system­field interaction model by means of

  

Source: Altafini, Claudio - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

 

Collections: Engineering; Mathematics