88 research outputs found
Why must we work in the phase space?
We are going to prove that the phase-space description is fundamental both in
the classical and quantum physics. It is shown that many problems in
statistical mechanics, quantum mechanics, quasi-classical theory and in the
theory of integrable systems may be well-formulated only in the phase-space
language.Comment: 130 page
Improvement by laser quenching of an "atom diode": a one-way barrier for ultra-cold atoms
Different laser devices working as ``atom diodes'' or ``one-way barriers''
for ultra-cold atoms have been proposed recently. They transmit ground state
level atoms coming from one side, say from the left, but reflect them when they
come from the other side. We combine a previous model, consisting of the
stimulated Raman adiabatic passage (STIRAP) from the ground to an excited state
and a state-selective mirror potential, with a localized quenching laser which
produces spontaneous decay back to the ground state. This avoids backwards
motion, provides more control of the decay process and therefore a more compact
and useful device.Comment: 6 page
Quantization and noiseless measurements
In accordance with the fact that quantum measurements are described in terms
of positive operator measures (POMs), we consider certain aspects of a
quantization scheme in which a classical variable is associated
with a unique positive operator measure (POM) , which is not necessarily
projection valued. The motivation for such a scheme comes from the well-known
fact that due to the noise in a quantum measurement, the resulting outcome
distribution is given by a POM and cannot, in general, be described in terms of
a traditional observable, a selfadjoint operator. Accordingly, we notice that
the noiseless measurements are the ones which are determined by a selfadjoint
operator. The POM in our quantization is defined through its moment
operators, which are required to be of the form , , with
a fixed map from classical variables to Hilbert space operators. In
particular, we consider the quantization of classical \emph{questions}, that
is, functions taking only values 0 and 1. We compare two concrete
realizations of the map in view of their ability to produce noiseless
measurements: one being the Weyl map, and the other defined by using phase
space probability distributions.Comment: 15 pages, submitted to Journal of Physics
Coherent States Measurement Entropy
Coherent states (CS) quantum entropy can be split into two components. The
dynamical entropy is linked with the dynamical properties of a quantum system.
The measurement entropy, which tends to zero in the semiclassical limit,
describes the unpredictability induced by the process of a quantum approximate
measurement. We study the CS--measurement entropy for spin coherent states
defined on the sphere discussing different methods dealing with the time limit
. In particular we propose an effective technique of computing
the entropy by iterated function systems. The dependence of CS--measurement
entropy on the character of the partition of the phase space is analysed.Comment: revtex, 22 pages, 14 figures available upon request (e-mail:
[email protected]). Submitted to J.Phys.
Some Properties of Transforms in Culture Theory
It is shown that, in certain circumstances, systems of cultural rules may be
represented by doubly stochastic matrices denoted called possibility
transforms, and by certain real valued possibility densities with inner
product. Using such objects we may characterize a certain problem of
ethnographic and ethological description as a problem of prediction, in which
observations are predicted by properties of fixed points of transforms of pure
systems, or by properties of convex combinations of such pure systems. That is,
ethnographic description is an application of the Birkhoff theorem regarding
doubly stochastic matrices on a space whose vertices are permutations.Comment: Read at International Quantum Structures Association meetings, 200
Informationally complete measurements and groups representation
Informationally complete measurements on a quantum system allow to estimate
the expectation value of any arbitrary operator by just averaging functions of
the experimental outcomes. We show that such kind of measurements can be
achieved through positive-operator valued measures (POVM's) related to unitary
irreducible representations of a group on the Hilbert space of the system. With
the help of frame theory we provide a constructive way to evaluate the
data-processing function for arbitrary operators.Comment: 9 pages, no figures, IOP style. Some new references adde
Scattering of two-level atoms by delta lasers: Exactly solvable models in atom optics
We study the scattering of two-level atoms at narrow laser fields, modeled by
a -shape intensity profile. The unique properties of these potentials
allow us to give simple analytic solutions for one or two field zones. Several
applications are studied: a single -laser may serve as a detector model
for atom detection and arrival-time measurements, either by means of
fluorescence or variations in occupation probabilities. We show that, in
principle, this ideal detector can measure the particle density, the quantum
mechanical flux, arrival time distributions or local kinetic energy densities.
Moreover, two spatially separated -lasers are used to investigate
quantized-motion effects on Ramsey interferometry.Comment: 11 pages, 5 figure
Symmetric Informationally Complete Measurements of Arbitrary Rank
There has been much interest in so-called SIC-POVMs: rank 1 symmetric
informationally complete positive operator valued measures. In this paper we
discuss the larger class of POVMs which are symmetric and informationally
complete but not necessarily rank 1. This class of POVMs is of some independent
interest. In particular it includes a POVM which is closely related to the
discrete Wigner function. However, it is interesting mainly because of the
light it casts on the problem of constructing rank 1 symmetric informationally
complete POVMs. In this connection we derive an extremal condition alternative
to the one derived by Renes et al.Comment: Contribution to proceedings of International Conference on Quantum
Optics, Minsk, 200
Optimal atomic detection by control of detuning and spatial dependence of laser intensity
Atomic detection by fluorescence may fail because of reflection from the
laser or transmission without excitation. The detection probability for a given
velocity range may be improved by controlling the detuning and the spatial
dependence of the laser intensity. A simple optimization method is discussed
and exemplified
Perspectives: Quantum Mechanics on Phase Space
The basic ideas in the theory of quantum mechanics on phase space are
illustrated through an introduction of generalities, which seem to underlie
most if not all such formulations and follow with examples taken primarily from
kinematical particle model descriptions exhibiting either Galileian or
Lorentzian symmetry. The structures of fundamental importance are the relevant
(Lie) groups of symmetries and their homogeneous (and associated) spaces that,
in the situations of interest, also possess Hamiltonian structures. Comments
are made on the relation between the theory outlined and a recent paper by
Carmeli, Cassinelli, Toigo, and Vacchini.Comment: "Quantum Structures 2004" - Meeting of the International Quantum
Structures Association; Denver, Colorado; 17-22 July, 200
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