205 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
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
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
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
Coherence lifetimes of excitations in an atomic condensate due to the thin spectrum
We study the quantum coherence properties of a finite sized atomic condensate
using a toy-model and the thin spectrum model formalism. The decoherence time
for a condensate in the ground state, nominally taken as a variational symmetry
breaking state, is investigated for both zero and finite temperatures. We also
consider the lifetimes for Bogoliubov quasi-particle excitations, and contrast
them to the observability window determined by the ground state coherence time.
The lifetimes are shown to exhibit a general characteristic dependence on the
temperature, determined by the thin spectrum accompanying the spontaneous
symmetry breaking ground state
SU(1,1) symmetry of multimode squeezed states
We show that a class of multimode optical transformations that employ linear
optics plus two-mode squeezing can be expressed as SU(1,1) operators. These
operations are relevant to state-of-the-art continuous variable quantum
information experiments including quantum state sharing, quantum teleportation,
and multipartite entangled states. Using this SU(1,1) description of these
transformations, we obtain a new basis for such transformations that lies in a
useful representation of this group and lies outside the often-used restriction
to Gaussian states. We analyze this basis, show its application to a class of
transformations, and discuss its extension to more general quantum optical
networks
Husimi Transform of an Operator Product
It is shown that the series derived by Mizrahi, giving the Husimi transform
(or covariant symbol) of an operator product, is absolutely convergent for a
large class of operators. In particular, the generalized Liouville equation,
describing the time evolution of the Husimi function, is absolutely convergent
for a large class of Hamiltonians. By contrast, the series derived by
Groenewold, giving the Weyl transform of an operator product, is often only
asymptotic, or even undefined. The result is used to derive an alternative way
of expressing expectation values in terms of the Husimi function. The advantage
of this formula is that it applies in many of the cases where the anti-Husimi
transform (or contravariant symbol) is so highly singular that it fails to
exist as a tempered distribution.Comment: AMS-Latex, 13 page
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