scholarly journals Generalizedq-deformed Tamm-Dancoff oscillator algebra and associated coherent states

2014 ◽  
Vol 55 (8) ◽  
pp. 081702 ◽  
Author(s):  
Won Sang Chung ◽  
Mahouton Norbert Hounkonnou ◽  
Sama Arjika
Keyword(s):  
Coherent States ◽  
Oscillator Algebra

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

scholarly journals Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Kevin Zelaya ◽  
Oscar Rosas-Ortiz ◽  
Zurika Blanco-Garcia ◽  
Sara Cruz y Cruz
Keyword(s):  
Coherent States ◽  
Beam Splitter ◽  
Delta Function ◽  
Oscillator Algebra ◽  
Closure Relation ◽  
Classical Analog ◽  
Delta Distribution ◽  
Nonclassical Properties ◽  
Generalized Oscillator ◽  
Oscillator Algebras

The purposes of this work are (1) to show that the appropriate generalizations of the oscillator algebra permit the construction of a wide set of nonlinear coherent states in unified form and (2) to clarify the likely contradiction between the nonclassical properties of such nonlinear coherent states and the possibility of finding a classical analog for them since they are P-represented by a delta function. In (1) we prove that a class of nonlinear coherent states can be constructed to satisfy a closure relation that is expressed uniquely in terms of the Meijer G-function. This property automatically defines the delta distribution as the P-representation of such states. Then, in principle, there must be a classical analog for them. Among other examples, we construct a family of nonlinear coherent states for a representation of the su(1,1) Lie algebra that is realized as a deformation of the oscillator algebra. In (2), we use a beam splitter to show that the nonlinear coherent states exhibit properties like antibunching that prohibit a classical description for them. We also show that these states lack second-order coherence. That is, although the P-representation of the nonlinear coherent states is a delta function, they are not full coherent. Therefore, the systems associated with the generalized oscillator algebras cannot be considered “classical” in the context of the quantum theory of optical coherence.

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.

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

COHERENT STATES FOR NONLINEAR TWO-BOSON REALIZATION OF THE ISOTROPIC OSCILLATOR ALGEBRA ON A SPHERE

2013 ◽  
Vol 10 (07) ◽  
pp. 1350028 ◽  
Author(s):  
A. MAHDIFAR
Keyword(s):  
Quantum Entanglement ◽  
Coherent States ◽  
Physical Space ◽  
Statistical Properties ◽  
Oscillator Algebra ◽  
Deformation Function ◽  
Boson Realization ◽  
Nonclassical Properties ◽  
Quantum Statistical

In this paper, we generalize Schwinger realization of the 𝔰𝔲(2) algebra to construct a two-mode realization for deformed 𝔰𝔲(2) algebra on a sphere. We obtain a nonlinear (f-deformed) Schwinger realization with a deformation function corresponding to the curvature of sphere that in the flat limit tends to unity. With the use of this nonlinear two-mode algebra, we construct the associated two-mode coherent states (CSs) on the sphere and investigate their quantum entanglement. We also compare the quantum statistical properties of the two modes of the constructed CSs, including anticorrelation and antibunching effects. Particularly, the influence of the curvature of the physical space on the nonclassical properties of two modes is clarified.

The symmetric q-oscillator algebra: q-coherent states, q-Bargmann–Fock realization and continuous q-Hermite polynomials with 0 < q < 1

2016 ◽  
Vol 13 (03) ◽  
pp. 1650028 ◽  
Author(s):  
H. Fakhri ◽  
A. Hashemi
Keyword(s):  
Text Analysis ◽  
Coherent States ◽  
Hermite Polynomials ◽  
Representation Space ◽  
Oscillator Algebra ◽  
Fock Representation ◽  
Minimum Uncertainty

The symmetric [Formula: see text]-analysis is used to construct a type of minimum-uncertainty [Formula: see text]-coherent states in the Fock representation space of the symmetric [Formula: see text]-oscillator ∗-algebra with [Formula: see text]. Then, its corresponding [Formula: see text]-Hermite polynomials are derived by using the [Formula: see text]-Bargmann–Fock realization of the symmetric [Formula: see text]-oscillator algebra.

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