On a family of photon-added deformed coherent states associated with two-parameter deformed boson oscillator algebra

2004 ◽  
Vol 82 (8) ◽  
pp. 623-646 ◽  
Author(s):  
M H Naderi ◽  
M Soltanolkotabi ◽  
R Roknizadeh
Keyword(s):  
Coherent States ◽  
Photon Number ◽  
Dimensional Subspace ◽  
Oscillator Algebra ◽  
Infinite Dimensional ◽  
Quadrature Squeezing ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra ◽  
Two Parameter ◽  
Infinite Dimensional Subspace

By introducing a generalization of the (p, q)-deformed boson oscillator algebra, we establish a two-parameter deformed oscillator algebra in an infinite-dimensional subspace of the Hilbert space of a harmonic oscillator without first finite Fock states. We construct the associated coherent states, which can be interpreted as photon-added deformed states. In addition to the mathematical characteristics, the quantum statistical properties of these states are discussed in detail analytically and numerically in the context of conventional as well as deformed quantum optics. Particularly, we find that for conventional (nondeformed) photons the states may be quadrature squeezed in both cases Q = pq < 1, Q = pq > 1 and their photon number statistics exhibits a transition from sub-Poissonian to super-Poissonian for Q < 1 whereas for Q > 1 they are always sub-Poissonian. On the other hand, for deformed photons, the states are sub-Poissonian for Q > 1 and no quadrature squeezing occurs while for Q < 1 they show super-Poissonian behavior and there is a simultaneous squeezing in both field quadratures.PACS Nos.: 42.50.Ar, 03.65.–w

Solution of the Dirac equation with some superintegrable potentials by the quadratic algebra approach

2014 ◽  
Vol 29 (06) ◽  
pp. 1450028 ◽  
Author(s):  
S. Aghaei ◽  
A. Chenaghlou
Keyword(s):  
Dirac Equation ◽  
Quadratic Algebra ◽  
Two Dimensional ◽  
Oscillator Algebra ◽  
Quadratic Algebras ◽  
Energy Eigenvalues ◽  
Vector Potentials ◽  
Algebra Approach ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

The Dirac equation with scalar and vector potentials of equal magnitude is considered. For the two-dimensional harmonic oscillator superintegrable potential, the superintegrable potentials of E8 (case (3b)), S4 and S2, the Schrödinger-like equations are studied. The quadratic algebras of these quasi-Hamiltonians are derived. By using the realization of the quadratic algebras in a deformed oscillator algebra, the structure function and the energy eigenvalues are obtained.

scholarly journals THREE-PARAMETER (TWO-SIDED) DEFORMATION OF HEISENBERG ALGEBRA

2012 ◽  
Vol 27 (21) ◽  
pp. 1250114 ◽  
Author(s):  
A. M. GAVRILIK ◽  
I. I. KACHURIK
Keyword(s):  
Deformation Parameter ◽  
Particle Number ◽  
Heisenberg Algebra ◽  
Unusual Property ◽  
Oscillator Algebra ◽  
Number Operator ◽  
The Third ◽  
Defining Relation ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

A three-parametric two-sided deformation of Heisenberg algebra (HA), with p, q-deformed commutator in the L.H.S. of basic defining relation and certain deformation of its R.H.S., is introduced and studied. The third deformation parameter μ appears in an extra term in the R.H.S. as pre-factor of Hamiltonian. For this deformation of HA we find novel properties. Namely, we prove it is possible to realize this (p, q, μ)-deformed HA by means of some deformed oscillator algebra. Also, we find the unusual property that the deforming factor μ in the considered deformed HA inevitably depends explicitly on particle number operator N. Such a novel N-dependence is special for the two-sided deformation of HA treated jointly with its deformed oscillator realizations.

Necessary and Sufficient Conditions for the Equality of L(f) and l1

1982 ◽  
Vol 34 (2) ◽  
pp. 406-410 ◽  
Author(s):  
Waleed Deeb
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Sufficient Conditions ◽  
Dimensional Subspace ◽  
Locally Convex Space ◽  
Natural Question ◽  
Infinite Dimensional ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Infinite Dimensional Subspace

Introduction. Let f be a modulus, ei = (δij) and E = {ei, i = 1, 2, …}. The L(f) spaces were created (to the best of our knowledge) by W. Ruckle in [2] in order to construct an example to answer a question of A. Wilansky. It turned out that these spaces are interesting spaces. For example lp, 0 < p ≦ 1 is an L(f) space with f(x) = xp, and every FK space contains an L(f) space [2]. A natural question is: For which f is L(f) a locally convex space? It is known that L(f) ⊆ l1, for all f modulus (see [2]), and l1 is the smallest locally convex FK space in which E is bounded (see [1]). Thus the question becomes: For which f does L(f) equal l1? In this paper we characterize such f. (An FK space need not be locally convex here.) We also characterize those f for which L(f) contains a convex ball. The final result of this paper is to show that if f satisfies f(x · y) ≦ f(x) · f(y) and L(f) ≠ l1 then L(f) contains no infinite dimensional subspace isomorphic to a Banach space.

Photon-catalyzed optical coherent states generated via a non-degenerate parametric amplifier with quantum-optical catalysis

2020 ◽  
Vol 98 (2) ◽  
pp. 119-124 ◽  
Author(s):  
Hong-Chun Yuan ◽  
Xue-Xiang Xu ◽  
Heng-Mei Li ◽  
Ye-Jun Xu ◽  
Xiang-Guo Meng
Keyword(s):  
Coherent State ◽  
Wigner Function ◽  
Coherent States ◽  
Laguerre Polynomial ◽  
Photon Number ◽  
Parametric Amplifier ◽  
Normalization Factor ◽  
Nonclassical Properties ◽  
Quadrature Squeezing ◽  
Quantum Optical

We theoretically generate a kind of photon-catalyzed optical coherent states (PCOCSs) by heralded interference between any photons and coherent state via a non-degenerate parametric amplifier, which is also just a Laguerre polynomial excited coherent state. Based on obtaining the probability of successfully detecting them (also the normalization factor), the nonclassical properties of the PCOCSs are analytically investigated according to autocorrelation function, quadrature squeezing, and the negativity of the Wigner function. It is found that the nonclassicality depends on the amplitude of the coherent state, the catalysis photon number, and amplifier parameter. The negative volume of their Wigner function can be enlarged by increasing the catalysis photon number. These parameters may be effectively used to improve and enhance the nonclassical characteristics.

Representations of the deformed oscillator algebra for different choices of generators

2000 ◽  
Vol 100 (2) ◽  
pp. 2061-2076 ◽  
Author(s):  
V. V. Borzov ◽  
E. V. Damaskinskii ◽  
S. B. Yegorov
Keyword(s):  
Oscillator Algebra ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

GENERALIZED DEFORMED HARMONIC OSCILLATORS IN THE FRAMEWORK OF UNIFIED (q; α, β, γ; ν)-DEFORMATION

2010 ◽  
Vol 25 (15) ◽  
pp. 1239-1249 ◽  
Author(s):  
I. M. BURBAN
Keyword(s):  
Coherent States ◽  
Anharmonic Oscillator ◽  
Harmonic Oscillators ◽  
Kerr Medium ◽  
Oscillator Algebra ◽  
Special Values ◽  
Deformation Parameters ◽  
Deformed Oscillator

The aim of this paper is the study of the generalized deformed quantum oscillators in the framework (q; α, β, γ; ν)-deformed of oscillator algebra. By selecting the special values of deformation parameters, we have separated a generalized deformed oscillator connected with generalized discrete Hermite II polynomials. By these means we have constructed Barut–Girardello type coherent states of this oscillator. We have found the conditions on the (q; α, β, γ; ν)-deformation parameters at which the free (q; α, β, γ; ν)-deformed oscillator approximate the usual anharmonic oscillator in the homogeneous Kerr medium.

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