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Journal of Physics A Mathematical and General

A continuous counting observation and posterior quantum dynamics

V. P. Belavkin

Published Dec 7, 1989• 87 citations
Publisher

Abstract

A stochastic model for a continuous photon counting measurement is proposed. An equation for the generating functional of the statistics of counts is found. A stochastic linear equation for the unnormalised posterior state vector of atoms, continuously collapsing without mixing, is derived by using quantum stochastic calculus methods.
DOI
10.1088/0305-4470/22/23/006

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We analyze a simultaneous continuous measurement of photon-counting and homodyne detection. The stochastic master equation or stochastic Schrödinger equation describing the measurement process includes both jump-type and diffusive-type stochastic increments. Analytic expressions of the wave function conditioned on homodyne and photon-counting records are obtained, yielding the probability density distributions and generating functions of the measurement records. Formula for the expectation values of the homodyne records conditioned on a photon-counting event is also derived which quantitatively describes the measurement backaction of photon-counting on the homodyne output. The obtained results are applied to typical initial states --- coherent, number, thermal, and squeezed states. Monte Carlo simulations of the measurement processes are also presented to demonstrate the dynamics of the combined measurement process.
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