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2013 | 1 | 34-56
Article title

Quantum continuous measurements: The stochastic
Schrödinger equations and the spectrum of the output

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EN
Abstracts
EN
The stochastic Schrödinger 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 diffusive case. Firstly, we discuss the quantum
stochastic Schrödinger equation, which is based on quantum
stochastic calculus, and we show how to transform it into
the classical stochastic Schrödinger equation by diagonalization
of suitable commuting quantum observables. 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 Schrödinger equation.
Moreover, the relation with quantum filtering theory is shortly
discussed. 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 two-level atom stimulated by a laser, to
discuss the differences between homodyne and heterodyne
detection and to explicitly show squeezing and anti-squeezing
of the homodyne spectrum and the Mollow triplet in the fluorescence
spectrum.
Publisher
Year
Volume
1
Pages
34-56
Physical description
Dates
accepted
12 - 6 - 2013
online
13 - 08 - 2013
received
16 - 01 - 2013
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Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_qmetro-2013-0005
Identifiers
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