366 research outputs found
Properties of Squeezed-State Excitations
The photon distribution function of a discrete series of excitations of
squeezed coherent states is given explicitly in terms of Hermite polynomials of
two variables. The Wigner and the coherent-state quasiprobabilities are also
presented in closed form through the Hermite polynomials and their limiting
cases. Expectation values of photon numbers and their dispersion are
calculated. Some three-dimensional plots of photon distributions for different
squeezing parameters demonstrating oscillatory behaviour are given.Comment: Latex,35 pages,submitted to Quant.Semiclassical Op
On Bargmann Representations of Wigner Function
By using the localized character of canonical coherent states, we give a
straightforward derivation of the Bargmann integral representation of Wigner
function (W). A non-integral representation is presented in terms of a
quadratic form V*FV, where F is a self-adjoint matrix whose entries are
tabulated functions and V is a vector depending in a simple recursive way on
the derivatives of the Bargmann function. Such a representation may be of use
in numerical computations. We discuss a relation involving the geometry of
Wigner function and the spacial uncertainty of the coherent state basis we use
to represent it.Comment: accepted for publication in J. Phys. A: Math. and Theo
Wigner function evolution in self-Kerr Medium derived by Entangled state representation
By introducing the thermo entangled state representation, we convert the
calculation of Wigner function (WF) of density operator to an overlap between
"two pure" states in a two-mode enlarged Fock space. Furthermore, we derive a
new WF evolution formula of any initial state in self-Kerr Medium with photon
loss and find that the photon number distribution for any initial state is
independent of the coupling factor with Kerr Medium, where the number state is
not affected by the Kerr nonlinearity and evolves into a density operator of
binomial distribution.Comment: 9 pages, 1 figur
Quantum mechanical photon-count formula derived by entangled state representation
By introducing the thermo entangled state representation, we derived four new
photocount distribution formulas for a given density operator of light field.
It is shown that these new formulas, which is convenient to calculate the
photocount, can be expressed as such integrations over Laguree-Gaussian
function with characteristic function, Wigner function, Q-function, and
P-function, respectively.Comment: 5 pages, no figur
Lorentz Beams
A new kind of tridimensional scalar optical beams is introduced. These beams
are called Lorentz beams because the form of their transverse pattern in the
source plane is the product of two independent Lorentz functions. Closed-form
expression of free-space propagation under paraxial limit is derived and pseudo
non-diffracting features pointed out. Moreover, as the slowly varying part of
these fields fulfils the scalar paraxial wave equation, it follows that there
exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original
Lorentz beam to a Gaussian apodization function. Although the existence of
Lorentz-Gauss beams can be shown by using two different and independent ways
obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega
et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different
approach, which makes use of Lie's group theory, and which possesses the merit
to put into evidence the symmetries present in paraxial Optics.Comment: 11 pages, 1 figure, submitted to Journal of Optics
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
Comment on "Single-mode excited entangled coherent states"
In Xu and Kuang (\textit{J. Phys. A: Math. Gen.} 39 (2006) L191), the authors
claim that, for single-mode excited entangled coherent states , \textquotedblleft the photon excitations lead to the
decrease of the concurrence in the strong field regime of and
the concurrence tends to zero when ". This is wrong.Comment: 4 apges, 2 figures, submitted to JPA 15 April 200
A Contribution to the Solid State Forms of Bis(demethoxy)curcumin: Co-Crystal Screening and Characterization
Bis(demethoxy)curcumin (BDMC) is one of the main active components found in turmeric. Major drawbacks for its usage are its low aqueous solubility, and the challenging separation from other curcuminoids present in turmeric. Co-crystallization can be applied to alter the physicochemical properties of BDMC in a desired manner. A co-crystal screening of BDMC with four hydroxybenzenes was carried out using four different methods of co-crystal production: crystallization from solution by slow solvent evaporation (SSE), and rapid solvent removal (RSR), liquid-assisted grinding (LAG), and crystallization from the melt phase. Two co-crystal phases of BDMC were obtained with pyrogallol (PYR), and hydroxyquinol (HYQ). PYR-BDMC co-crystals can be obtained only from the melt, while HYQ-BDMC co-crystals could also be produced by LAG. Both co-crystals possess an equimolar composition and reveal an incongruent melting behavior. Infrared spectroscopy demonstrated the presence of BDMC in the diketo form in the PYR co-crystals, while it is in a more stable keto-enol form in the HYQ co-crystals. Solubility measurements in ethanol and an ethanol-water mixture revealed an increase of solubility in the latter, but a slightly negative effect on ethanol solubility. These results are useful for a prospective development of crystallization-based separation processes of chemical similar substances through co-crystallization
Radon transform and pattern functions in quantum tomography
The two-dimensional Radon transform of the Wigner quasiprobability is
introduced in canonical form and the functions playing a role in its inversion
are discussed. The transformation properties of this Radon transform with
respect to displacement and squeezing of states are studied and it is shown
that the last is equivalent to a symplectic transformation of the variables of
the Radon transform with the contragredient matrix to the transformation of the
variables in the Wigner quasiprobability. The reconstruction of the density
operator from the Radon transform and the direct reconstruction of its
Fock-state matrix elements and of its normally ordered moments are discussed.
It is found that for finite-order moments the integration over the angle can be
reduced to a finite sum over a discrete set of angles. The reconstruction of
the Fock-state matrix elements from the normally ordered moments leads to a new
representation of the pattern functions by convergent series over even or odd
Hermite polynomials which is appropriate for practical calculations. The
structure of the pattern functions as first derivatives of the products of
normalizable and nonnormalizable eigenfunctions to the number operator is
considered from the point of view of this new representation.Comment: To appear on Journal of Modern Optics.Submitted t
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