COHERENT STATE OF α-DEFORMED WEYL–HEISENBERG ALGEBRA

2013 ◽  
Vol 10 (05) ◽  
pp. 1350014 ◽  
Author(s):  
SH. DEHDASHTI ◽  
A. MAHDIFAR ◽  
R. ROKNIZADEH
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Heisenberg Algebra ◽  
Statistical Properties ◽  
Potential Well ◽  
Mandel Parameter ◽  
Boson Realization ◽  
Deformed Algebra

At first, we introduce α-deformed algebra as a kind of generalization of the Weyl–Heisenberg algebra so that we get the su(2)- and su(1, 1)-algebras whenever α has specific values. After that, we construct coherent states of this algebra. Third, a realization of this algebra is given in the system of a harmonic oscillator confined at the center of a potential well. Then, we introduce two-boson realization of the α-deformed Weyl–Heisenberg algebra and use this representation to write α-deformed coherent states in terms of the two modes number states. Following these points, we consider mean number of excitations (we call them in general photons) and Mandel parameter as statistical properties of the α-deformed coherent states. Finally, the Fubini–Study metric is calculated for the α-coherent states manifold.

COHERENT STATES AND SCHWINGER MODELS FOR PSEUDO GENERALIZATION OF THE HEISENBERG ALGEBRA

2009 ◽  
Vol 24 (25) ◽  
pp. 2039-2051 ◽  
Author(s):  
H. FAKHRI ◽  
B. MOJAVERI ◽  
A. DEHGHANI
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Heisenberg Algebra ◽  
Creation And Annihilation Operators ◽  
Number Of Generators ◽  
Simple Harmonic Oscillator

We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with [Formula: see text] and [Formula: see text] symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are [Formula: see text]-pseudo-Hermiticity and [Formula: see text]-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.

On the Squeezing and Displacement of nth-Order

1997 ◽  
Vol 11 (09n10) ◽  
pp. 399-406
Author(s):  
Norton G. de Almeida ◽  
Célia M. A. Dantas
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Photon Number ◽  
Natural Generalization ◽  
Statistical Properties ◽  
Number Distribution ◽  
Quantum Statistical ◽  
Photon Number Distribution

The norder expressions for the squeezed and coherent states are derived as a natural generalization of the usual squeezed coherent and coherent states. The photon number distribution of n order of squeezed coherent states that are eigenstates of the operators [Formula: see text] is derived. The n order coherent state is a particular case of the states that we are now deriving. Some mathematical and quantum statistical properties of these states are discussed.

scholarly journals COHERENT STATE OF THE EFFECTIVE MASS HARMONIC OSCILLATOR

2009 ◽  
Vol 24 (17) ◽  
pp. 1343-1353 ◽  
Author(s):  
ATREYEE BISWAS ◽  
BARNANA ROY
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Closed Form ◽  
Effective Mass ◽  
Coherent States ◽  
Mass Function ◽  
Wigner Functions

We construct coherent state of the effective mass harmonic oscillator and examine some of its properties. In particular closed form expressions of coherent states for different choices of the mass function are obtained and it is shown that such states are not in general x - p uncertainty states. We also compute the associated Wigner functions.

scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

scholarly journals ON A GENERAL FORMALISM OF NONLINEAR CHARGE COHERENT STATES, THEIR QUANTUM STATISTICS AND NONCLASSICAL PROPERTIES

2010 ◽  
Vol 25 (17) ◽  
pp. 3481-3504 ◽  
Author(s):  
F. EFTEKHARI ◽  
M. K. TAVASSOLY
Keyword(s):  
Coherent States ◽  
Nonclassical States ◽  
Mandel Parameter ◽  
Physical Systems ◽  
Nonclassical Properties ◽  
Deformed Algebra ◽  
Solvable Quantum ◽  
Antibunching Effect ◽  
Quantum Statistical ◽  
Special Case

In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coherent states. The su Q(1, 1) algebra as a nonlinear deformed algebra realization of the introduced states is established. In addition, the corresponding even and odd nonlinear charge coherent states have also been introduced. The formalism has the potentiality to be applied to systems either with known "nonlinearity function" f(n) or solvable quantum system with known "discrete nondegenerate spectrum" en. As some physical appearances, a few known physical systems in the two mentioned categories have been considered. Finally, since the construction of nonclassical states is a central topic of quantum optics, nonclassical features and quantum statistical properties of the introduced states have been investigated by evaluating single- and two-mode squeezing, su (1, 1)-squeezing, Mandel parameter and antibunching effect (via g-correlation function) as well as some of their generalized forms we have introduced in the present paper.

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.

PERELOMOV AND BARUT–GIRARDELLO SU(1, 1) COHERENT STATES FOR HARMONIC OSCILLATOR IN ONE-DIMENSIONAL HALF SPACE

2006 ◽  
Vol 21 (12) ◽  
pp. 2635-2644 ◽  
Author(s):  
Q. H. LIU ◽  
H. ZHUO
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Half Space ◽  
Ground State ◽  
Classical Limit ◽  
Coherent States ◽  
Mean Values ◽  
One Dimensional ◽  
The Mean

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

Angular momentum coherent states

1971 ◽  
Vol 321 (1546) ◽  
pp. 321-340 ◽  
Keyword(s):  
Angular Momentum ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Classical Limit ◽  
Coherent States ◽  
Uncertainty Relations ◽  
Mean Square ◽  
Expectation Values ◽  
Angular Momenta ◽  
Two Component

The work of Carruthers & Nieto on the harmonic oscillator coherent states is combined with Schwinger’s construction of angular momentum to produce the angular momentum coherent states. It is shown that these states become the vector representatives of angular momentum in the classical limit, and so are particularly useful for discussing the transition from quantum to classical angular momentum. The uncertainty relations for angle and angular momentum are described and are compatible with the classical limit. Under rotations the coherent states transform in a manner that in the classical limit is equivalent to the transformation of vectors, and in the same limit the root mean square variation of the expectation values of the components of angular momentum become negligible in comparison with the expectation values themselves. The coupling of two angular momenta in the classical limit is investigated: it is shown that although the product of two coherent states is not itself a coherent state, it does represent a packet similar to a true coherent state, and centred on the direction of the classical resultant of the two component vectors. The properties and implications of hyperbolic angular momentum space are discussed.

COHERENT STATES OF NONCONSERVATIVE HARMONIC OSCILLATOR WITH A SINGULAR PERTURBATION

2003 ◽  
Vol 17 (12) ◽  
pp. 2429-2437 ◽  
Author(s):  
JEONG RYEOL CHOI
Keyword(s):  
Singular Perturbation ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Mechanical Energy ◽  
Invariant Operator ◽  
Expectation Values ◽  
Raising Operators ◽  
The Difference

We investigated the coherent states of nonconservative harmonic oscillator with a singular perturbation. The invariant operator represented in terms of lowering and raising operators. We confirmed that if the difference between two eigenvalues, α and β, of coherent states is much larger than unity, the states |α> and |β> are approximately orthogonal to each another. We calculated the expectation values of various quantities such as invariant operator, Hamiltonian and mechanical energy in coherent state. The mechanical energy of the system described by the Kanai–Caldirola Hamiltonian decreased exponentially depending on γ as time goes by in coherent state.

Measure of non-Gaussianity for photon-added nonlinear coherent states

2018 ◽  
Vol 15 (09) ◽  
pp. 1850158
Author(s):  
K. Berrada ◽  
H. Eleuch
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Deformation Parameter ◽  
Critical Value ◽  
Statistical Properties ◽  
Noncommutative Space ◽  
Mandel’S Parameter ◽  
Generalized Coherent States ◽  
Non Gaussian

In this paper, we study the non-Gaussian character in generalized coherent states in the framework of a noncommutative space by adding photons to deformed coherent states, which is called the photon-added nonlinear coherent states (PANCSs). We find that the non-Gaussianity of PANCSs is enhanced with the increase of the photon-added number and it increases monotonically with the amplitude of the coherent states. Interestingly, we obtain that the maximal value of non-Gaussianity measure occurs at a certain critical value of the coherent state amplitude, where this critical value is determined by the kind of the deformation. Using the Mandel’s parameter, we examine the statistical properties for the PANCSs and show that the Mandel’s parameter may take positive and negative values depending on the choice of the amplitude and deformation parameter, exhibiting sub-Poissonian distribution and super-Poissonian distribution.

Sign in / Sign up

Export Citation Format

Share Document