58 research outputs found
Quantum stochastic equations for an opto-mechanical oscillator with radiation pressure interaction and non-Markovian effects
The quantum stochastic Schroedinger equation or Hudson-Parthasareathy (HP)
equation is a powerful tool to construct unitary dilations of quantum dynamical
semigroups and to develop the theory of measurements in continuous time via the
construction of output fields. An important feature of such an equation is that
it allows to treat not only absorption and emission of quanta, but also
scattering processes, which however had very few applications in physical
modelling. Moreover, recent developments have shown that also some
non-Markovian dynamics can be generated by suitable choices of the state of the
quantum noises involved in the HP-equation. This paper is devoted to an
application involving these two features, non-Markovianity and scattering
process. We consider a micro-mirror mounted on a vibrating structure and
reflecting a laser beam, a process giving rise to a radiation-pressure force on
the mirror. We show that this process needs the scattering part of the
HP-equation to be described. On the other side, non-Markovianity is introduced
by the dissipation due to the interaction with some thermal environment which
we represent by a phonon field, with a nearly arbitrary excitation spectrum,
and by the introduction of phase noise in the laser beam. Finally, we study the
full power spectrum of the reflected light and we show how the laser beam can
be used as a temperature probe.Comment: 17 page
Entropy and information gain in quantum continual measurements
The theory of measurements continuous in time in quantum mechanics (quantum
continual measurements) has been formulated by using the notions of instrument,
positive operator valued measure, etc., by using quantum stochastic
differential equations and by using classical stochastic differential equations
(SDE's) for vectors in Hilbert spaces or for trace-class operators. In the same
times Ozawa made developments in the theory of instruments and introduced the
related notions of a posteriori states and of information gain [1].
In this paper we introduce a simple class of SDE's relevant to the theory of
continual measurements and we recall how they are related to instruments and a
posteriori states and, so, to the general formulation of quantum mechanics.
Then we introduce and use the notion of information gain and the other results
of the paper [1] inside the theory of continual measurements.
[1] M. Ozawa, On information gain by quantum measurements of continuous
observables, J. Math. Phys. 27 (1986) 759-763.Comment: 8 pages. Submitted to Proceedings of "Quantum Communication,
Computing, and Measurements (Capri, Italy, July 2000)
Feedback control of the squeezing of the fluorescence light
Among the formulations of the theory of quantum measurements in continuous
time, quantum trajectory theory is very suitable for the introduction of
measurement based feedback and closed loop control of quantum systems. In this
paper we present such a construction in the concrete case of a two-level atom
stimulated by a coherent, monochromatic laser. In particular, we show how fast
feedback \`a la Wiseman and Milburn can be introduced in the formulation of the
theory. Then, the spectrum of the free fluorescence light is studied and
typical quantum phenomena, squeezing and sub-natural line-narrowing, are
presented.Comment: 10 pages, 3 figures. Submitted to proceedings of PhysCon0
On a class of stochastic differential equations used in quantum optics
Stochastic differential equations for processes with values in Hilbert spaces
are now largely used in the quantum theory of open systems. In this work we
present a class of such equations and discuss their main properties; moreover,
we explain how they are derived from purely quantum mechanical models, where
the dynamics is represented by a unitary evolution in a Hilbert space, and how
they are related to the theory of continual measurements. An essential tool is
an isomorphism between the bosonic Fock space and the Wiener space, which allow
to connect certain quantum objects with probabilistic ones.Comment: 13 pages, LaTeX2
Quantum measurements and entropic bounds on information transmission
While a positive operator valued measure gives the probabilities in a quantum
measurement, an instrument gives both the probabilities and the a posteriori
states. By interpreting the instrument as a quantum channel and by using the
monotonicity theorem for relative entropies many bounds on the classical
information extracted in a quantum measurement are obtained in a unified
manner. In particular, it is shown that such bounds can all be stated as
inequalities between mutual entropies. This approach based on channels gives
rise to a unified picture of known and new bounds on the classical information
(Holevo's, Shumacher-Westmoreland-Wootters', Hall's, Scutaru's bounds, a new
upper bound and a new lower one). Some examples clarify the mutual
relationships among the various bounds.Comment: 29 pages, 2 figures, uses qic.st
Quantum Langevin equations for optomechanical systems
We provide a fully quantum description of a mechanical oscillator in the
presence of thermal environmental noise by means of a quantum Langevin
formulation based on quantum stochastic calculus. The system dynamics is
determined by symmetry requirements and equipartition at equilibrium, while the
environment is described by quantum Bose fields in a suitable non-Fock
representation which allows for the introduction of temperature. A generic
spectral density of the environment can be described by introducing its state
trough a suitable P-representation. Including interaction of the mechanical
oscillator with a cavity mode via radiation pressure we obtain a description of
a simple optomechanical system in which, besides the Langevin equations for the
system, one has the exact input-output relations for the quantum noises. The
whole theory is valid at arbitrarily low temperature. This allows the exact
calculation of the stationary value of the mean energy of the mechanical
oscillator, as well as both homodyne and heterodyne spectra. The present
analysis allows in particular to study possible cooling scenarios and to obtain
the exact connection between observed spectra and fluctuation spectra of the
position of the mechanical oscillator.Comment: 37 pages, 2 figures. Major revisions; new reference
Instrumental processes, entropies, information in quantum continual measurements
In this paper we will give a short presentation of the quantum Levy-Khinchin
formula and of the formulation of quantum continual measurements based on
stochastic differential equations, matters which we had the pleasure to work on
in collaboration with Prof. Holevo. Then we will begin the study of various
entropies and relative entropies, which seem to be promising quantities for
measuring the information content of the continual measurement under
consideration and for analysing its asymptotic behaviour.Comment: 15 pages, requires Rinton-P9x6.cls. For the volume on the occasion of
Alexander Holevo's 60th birthda
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