72 research outputs found
Scaling Separability Criterion: Application To Gaussian States
We introduce examples of three- and four-mode entangled Gaussian mixed states
that are not detected by the scaling and Peres-Horodecki separability criteria.
The presented modification of the scaling criterion resolves this problem. Also
it is shown that the new criterion reproduces the main features of the scaling
pictures for different cases of entangled states, while the previous versions
lead to completely different outcomes. This property of the presented scheme is
evidence of its higher generality.Comment: 7 pages, 4 figure
Time-Dependent Invariants and Green's Functions in the Probability Representation of Quantum Mechanics
In the probability representation of quantum mechanics, quantum states are
represented by a classical probability distribution, the marginal distribution
function (MDF), whose time dependence is governed by a classical evolution
equation. We find and explicitly solve, for a wide class of Hamiltonians, new
equations for the Green's function of such an equation, the so-called classical
propagator. We elucidate the connection of the classical propagator to the
quantum propagator for the density matrix and to the Green's function of the
Schr\"odinger equation. Within the new description of quantum mechanics we give
a definition of coherence solely in terms of properties of the MDF and we test
the new definition recovering well known results. As an application, the forced
parametric oscillator is considered . Its classical and quantum propagator are
found, together with the MDF for coherent and Fock states.Comment: 29 pages, RevTex, 6 eps-figures, to appear on Phys. Rev.
Separability and entanglement of four-mode Gaussian states
The known Peres-Horodecki criterion and scaling criterion of separability are
considered on examples of three-mode and four-mode Gaussian states of
electromagnetic field. It is shown that the principal minors of the photon
quadrature dispersion matrix are sensitive to the change of scaling parameters.
An empirical observation has shown that the bigger the modulus of negative
principal minors, the more entangled the state.Comment: 14 pages, 11 figure
On calculating the mean values of quantum observables in the optical tomography representation
Given a density operator the optical tomography map defines a
one-parameter set of probability distributions on the real line allowing to reconstruct . We
introduce a dual map from the special class of quantum observables
to a special class of generalized functions such that the
mean value is given by the formula
. The class
includes all the symmetrized polynomials of canonical variables
and .Comment: 8 page
Energy-Sensitive and "Classical-like" Distances Between Quantum States
We introduce the concept of the ``polarized'' distance, which distinguishes
the orthogonal states with different energies. We also give new inequalities
for the known Hilbert-Schmidt distance between neighbouring states and express
this distance in terms of the quasiprobability distributions and the normally
ordered moments. Besides, we discuss the distance problem in the framework of
the recently proposed ``classical-like'' formulation of quantum mechanics,
based on the symplectic tomography scheme. The examples of the Fock, coherent,
``Schroedinger cats,'' squeezed, phase, and thermal states are considered.Comment: 23 pages, LaTex, 2 eps figures, to appear in Physica Script
Dynamics of entropy and nonclassical properties of the state of a -type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium
In this paper, we study the interaction between a three-level atom and a
quantized single-mode field with intensity-dependent coupling in a Kerr medium.
The three-level atom is considered to be in a -type configuration.
Under particular initial conditions, which may be prepared for the atom and
the field, the dynamical state vector of the entire system will be explicitly
obtained, for arbitrary nonlinearity function associated to any physical
system.
Then, after evaluating the variation of the field entropy against time, we
will investigate the quantum statistics as well as some of the nonclassical
properties of the introduced state. During our calculations we investigate the
effects of intensity-dependent coupling, Kerr medium and detuning parameters on
the depth and domain of the nonclassicality features of the atom-field state
vector. Finally, we compare our obtained results with those of -type
three-level atoms.Comment: 18 pages, 7 Figure
Tomographic Representation of Minisuperspace Quantum Cosmology and Noether Symmetries
The probability representation, in which cosmological quantum states are
described by a standard positive probability distribution, is constructed for
minisuperspace models selected by Noether symmetries. In such a case, the
tomographic probability distribution provides the classical evolution for the
models and can be considered an approach to select "observable" universes. Some
specific examples, derived from Extended Theories of Gravity, are worked out.
We discuss also how to connect tomograms, symmetries and cosmological
parameters.Comment: 15 page
Quantum singular oscillator as a model of two-ion trap: an amplification of transition probabilities due to small time variations of the binding potential
Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we
apply the quantum singular time dependent oscillator model to describe the
relative one dimensional motion of two ions in a trap. We argue that the model
can be justified for low energy excited states with the quantum numbers , provided that the dimensionless constant characterizing the
strength of the repulsive potential is large enough, . Time
dependent Gaussian-like wave packets generalizing odd coherent states of the
harmonic oscillator, and excitation number eigenstates are constructed. We show
that the relative motion of the ions, in contradistinction to its center of
mass counterpart, is extremely sensitive to the time dependence of the binding
harmonic potential, since the large value of results in a significant
amplification of the transition probabilities between energy eigenstate even
for slow time variations of the frequency.Comment: 19 pages, LaTeX, 5 eps-figures, to appear on Phys. Rev. A, one
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