Codice  QDD 145 
Titolo  Quantum continuous measurements: The stochastic Schroedinger equations and the spectrum of the output 
Data  20130117 
Autore/i  Barchielli, A.; Gregoratti, M. 
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Abstract  The stochastic Schroedinger equation, of classical or quantum type, allows to describe open quantum systems under measurement in continuous time. In this paper we review the link between these two descriptions and we study the properties of the output of the measurement. For simplicity we deal only with the diusive case. Firstly, we discuss the quantum stochastic Schroedinger equation, which is based on quantum stochastic calculus, and we show how to transform it into the classical stochastic Schroedinger equation by diagonalization of suitable quantum observables, based on the isomorphism between Fock space and Wiener space. Then, we give the a posteriori state, the conditional system state at time t given the output up to that time and we link its evolution to the classical stochastic Schroedinger equation. Finally, we study the output of the continuous measurement, which is a stochastic process with probability distribution given by the rules of quantum mechanics. When the output process is stationary, at least in the long run, the spectrum of the process can be introduced and its properties studied. In particular we show how the Heisenberg uncertainty relations give rise to characteristic bounds on the possible spectra and we discuss how this is related to the typical quantum phenomenon of squeezing. We use a simple quantum system, a twolevel atom stimulated by a laser, to discuss the dierences between homodyne and heterodyne detection and to explicitly show squeezing and antisqueezing and the Mollow triplet in the fluorescence spectrum. 
