New q -Hermite polynomials: characterization, operators algebra and associated coherent states

2015 ◽  
Vol 63 (1) ◽  
pp. 42-53
Author(s):  
Won Sang Chung ◽  
Mahouton Norbert Hounkonnou ◽  
Arjika Sama
Keyword(s):  
Coherent States ◽  
Hermite Polynomials ◽  
Operators Algebra

Nonclassicality of photon-modulated spin coherent states in the Holstein-Primakoff realization

2021 ◽  
Author(s):  
Xiaoyan Zhang ◽  
Jisuo Wang ◽  
Lei Wang ◽  
Xiangguo Meng ◽  
Baolong Liang
Keyword(s):  
Coherent States ◽  
Wigner Distribution ◽  
Hermite Polynomials ◽  
Photon Number ◽  
Spin Ladder ◽  
Bernoulli Distribution ◽  
Ladder Operators ◽  
Spin Number ◽  
Photon Number Distribution ◽  
Spin Coherent States

Abstract Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J ± on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.

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.

New approach to generating functions of single- and two-variable even- and odd-Hermite polynomials and applications in quantum optics

2014 ◽  
Vol 28 (32) ◽  
pp. 1450249 ◽  
Author(s):  
Fang Jia ◽  
Shuang Xu ◽  
Li-Yun Hu ◽  
Zhenglu Duan ◽  
Jie-Hui Huang
Keyword(s):  
Quantum Optics ◽  
Generating Functions ◽  
Coherent States ◽  
Hermite Polynomials ◽  
Quantum States ◽  
Iwop Technique ◽  
New Approach ◽  
The Iwop Technique ◽  
New Formula ◽  
Entangled Coherent States

Using the IWOP technique and completeness of representation, we obtain the integral expressions of single- and two-variable Hermite polynomials. Based on this, we further derive the generating functions of single- and two-variable even- and odd-Hermit polynomials. This method seems more concise and direct. In addition, some applications such as deriving new formula and constructing new two-mode quantum states are discussed. It is found that two-variable Hermite polynomials excitation can used to produce entangled coherent states.

A MODEL OF QUANTUM OSCILLATOR WITH DISCRETE SPACE

2008 ◽  
Vol 23 (13) ◽  
pp. 943-952
Author(s):  
I. I. KACHURYK ◽  
A. U. KLIMYK
Keyword(s):  
Real Line ◽  
Coherent States ◽  
Hermite Polynomials ◽  
Heisenberg Algebra ◽  
Discrete Space ◽  
Quantum Oscillator ◽  
Fock Representation ◽  
New Model

We construct a new model of the quantum oscillator, which is related to the discrete q-Hermite polynomials of the second type. The position and momentum operators in the model are appropriate operators of the Fock representation of a deformation of the Heisenberg algebra. These operators have a discrete non-degenerate spectra. These spectra are spread over the whole real line. Coordinate and momentum realizations of the model are constructed. Coherent states are explicitly given.

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