68 research outputs found
BALANCE EQUATIONS-BASED PROPERTIES OF THE RABI HAMILTONIAN
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate
observables. In this paper, we show how to deduce such quantitative links, named balance equations,
demonstrating as well their usefulness in bringing to light physical properties of the system without
solving the Schr¨odinger equation. The knowledge of such properties in the case of the Rabi Hamiltonian
is exploited to provide arguments to make easier the variational engineering of the ground state of this
model
Observation of a red-blue detuning asymmetry in matter-wave superradiance
We report the first experimental observations of strong suppression of
matter-wave superradiance using blue-detuned pump light and demonstrate a
pump-laser detuning asymmetry in the collective atomic recoil motion. In
contrast to all previous theoretical frameworks, which predict that the process
should be symmetric with respect to the sign of the pump-laser detuning, we
find that for condensates the symmetry is broken. With high condensate
densities and red-detuned light, the familiar distinctive multi-order,
matter-wave scattering pattern is clearly visible, whereas with blue-detuned
light superradiance is strongly suppressed. In the limit of a dilute atomic
gas, however, symmetry is restored.Comment: Accepted by Phys. Rev. Let
Inverse spin-s portrait and representation of qudit states by single probability vectors
Using the tomographic probability representation of qudit states and the
inverse spin-portrait method, we suggest a bijective map of the qudit density
operator onto a single probability distribution. Within the framework of the
approach proposed, any quantum spin-j state is associated with the
(2j+1)(4j+1)-dimensional probability vector whose components are labeled by
spin projections and points on the sphere. Such a vector has a clear physical
meaning and can be relatively easily measured. Quantum states form a convex
subset of the 2j(4j+3) simplex, with the boundary being illustrated for qubits
(j=1/2) and qutrits (j=1). A relation to the (2j+1)^2- and
(2j+1)(2j+2)-dimensional probability vectors is established in terms of spin-s
portraits. We also address an auxiliary problem of the optimum reconstruction
of qudit states, where the optimality implies a minimum relative error of the
density matrix due to the errors in measured probabilities.Comment: 23 pages, 4 figures, PDF LaTeX, submitted to the Journal of Russian
Laser Researc
Probability representation and quantumness tests for qudits and two-mode light states
Using tomographic-probability representation of spin states, quantum behavior
of qudits is examined. For a general j-qudit state we propose an explicit
formula of quantumness witnetness whose negative average value is incompatible
with classical statistical model. Probability representations of quantum and
classical (2j+1)-level systems are compared within the framework of quantumness
tests. Trough employing Jordan-Schwinger map the method is extended to check
quantumness of two-mode light states.Comment: 5 pages, 2 figures, PDFLaTeX, Contribution to the 11th International
Conference on Squeezed States and Uncertainty Relations (ICSSUR'09), June
22-26, 2009, Olomouc, Czech Republi
Unitary and Non-Unitary Matrices as a Source of Different Bases of Operators Acting on Hilbert Spaces
Columns of d^2 x N matrices are shown to create different sets of N operators
acting on -dimensional Hilbert space. This construction corresponds to a
formalism of the star-product of operator symbols. The known bases are shown to
be partial cases of generic formulas derived by using d^2 x N matrices as a
source for constructing arbitrary bases. The known examples of the SIC-POVM,
MUBs, and the phase-space description of qubit states are considered from the
viewpoint of the developed unified approach. Star-product schemes are
classified with respect to associated d^2 x N matrices. In particular, unitary
matrices correspond to self-dual schemes. Such self-dual star-product schemes
are shown to be determined by dequantizers which do not form POVM.Comment: 12 pages, 1 figure, 1 table, to appear in Journal of Russian Laser
Researc
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
Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics
Symmetric informationally complete positive operator valued measures
(SIC-POVMs) are studied within the framework of the probability representation
of quantum mechanics. A SIC-POVM is shown to be a special case of the
probability representation. The problem of SIC-POVM existence is formulated in
terms of symbols of operators associated with a star-product quantization
scheme. We show that SIC-POVMs (if they do exist) must obey general rules of
the star product, and, starting from this fact, we derive new relations on
SIC-projectors. The case of qubits is considered in detail, in particular, the
relation between the SIC probability representation and other probability
representations is established, the connection with mutually unbiased bases is
discussed, and comments to the Lie algebraic structure of SIC-POVMs are
presented.Comment: 22 pages, 1 figure, LaTeX, partially presented at the Workshop
"Nonlinearity and Coherence in Classical and Quantum Systems" held at the
University "Federico II" in Naples, Italy on December 4, 2009 in honor of
Prof. Margarita A. Man'ko in connection with her 70th birthday, minor
misprints are corrected in the second versio
Qubit portrait of the photon-number tomogram and separability of two-mode light states
In view of the photon-number tomograms of two-mode light states, using the
qubit-portrait method for studying the probability distributions with infinite
outputs, the separability and entanglement detection of the states are studied.
Examples of entangled Gaussian state and Schr\"{o}dinger cat state are
discussed.Comment: 20 pages, 6 figures, TeX file, to appear in Journal of Russian Laser
Researc
Frank-Condon principle and adjustment of optical waveguides with nonhomogeneous refractive indices
The adjustment of two different selfocs is considered using both exact
formulas for the mode-connection coefficients expressed in terms of Hermite
polynomials of several variables and a qualitative approach based on the
Frank-Condon principle. Several examples of the refractive-index dependence are
studied and illustrative plots for these examples are presented. The connection
with the tomographic approach to quantum states of a two-dimensional oscillator
and the Frank-Condon factors is established.Comment: 8 pages, 4 figures, published version (layout of figures changed,
typos corrected, references added
Classical Signal Model for Quantum Channels
Recently it was shown that the main distinguishing features of quantum
mechanics (QM) can be reproduced by a model based on classical random fields,
so called prequantum classical statistical field theory (PCSFT). This model
provides a possibility to represent averages of quantum observables, including
correlations of observables on subsystems of a composite system (e.g.,
entangled systems), as averages with respect to fluctuations of classical
(Gaussian) random fields. In this note we consider some consequences of PCSFT
for quantum information theory. They are based on the observation \cite{W} of
two authors of this paper that classical Gaussian channels (important in
classical signal theory) can be represented as quantum channels. Now we show
that quantum channels can be represented as classical linear transformations of
classical Gaussian signa
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