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Modern Physics Letters A

Zp-graded charge coherent states

Won Sang Chung

Published Jun 13, 2014• 2 citations
Publisher

Abstract

A new kind of charge coherent state called a Zp-graded charge coherent state is constructed by using the complex solution of the equation qp = 1. The p-1 charge operators are also explicitly constructed. We explicitly investigate some nonclassical properties for the Z3-graded charge coherent state.
DOI
10.1142/s0217732314501089

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•Sep 13, 2013•3 citations
In this paper, three-mode nonlinear coherent states are introduced by using the complex solution of the equation q3 = 1. The photon-added or photon-subtracted three-mode nonlinear coherent states are shown to be three-mode nonlinear coherent states with different nonlinear functions. The Z3-graded parity coherent states are introduced as examples of three-mode nonlinear coherent states. Finally, multi-mode coherent states and multi-mode nonlinear coherent states are also constructed in a similar way.
Two-mode charge (pair) coherent states have been introduced previously by using the 〈η| representation. In this paper, we reobtain these states by a rather different method. Then, using the nonlinear coherent state approach and based on a simple manner by which the representation of two-mode charge coherent states is introduced, we generalize the bosonic creation and annihilation operators to the f -deformed ladder operators and construct a new class of f -deformed charge coherent states. Unlike the (linear) pair coherent states, our presented structure has the potential to generate a large class of pair coherent states with various nonclassicality signs and physical properties which are of interest. For this purpose, we use a few well-known nonlinearity functions associated with particular quantum systems as some physical appearances of our presented formalism. After introducing the explicit form of the above correlated states in the two-mode Fock space, several nonclassicality features of the corresponding states (as well as the two-mode linear charge coherent states) are numerically investigated by calculating quadrature squeezing, the Mandel parameter, the second-order correlation function, the second-order correlation function between the two modes and the Cauchy–Schwartz inequality. Also, the oscillatory behaviour of the photon count and the quasi-probability (Husimi) function of the associated states will be discussed. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
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.
published in J. Phys. A37 (2004) 4361 Generalized Zk-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors. Recently in [1] we have constructed coherent states for k-fermions using Kerner’s [2] Z3-graded extension of the Grassmann variables [3]. These results were obtained in the case where the deformation parameter is a primitive cubic root of unity, i.e., k = 3. In order to obtain similar results in the generic case (by generic we mean here that q, the deformation parameter, is an arbitrary k th root of unity, i.e., for an arbitrary positive integer k) one should use Zk-graded generalizations of the Grassmann variables. Unfortunately, up to our knowledge, such structures have not been yet constructed in the spirit of Kerner’s variables. There exist however in the literature another point of view and other generalized Zk-graded Grassmann variables [4]. In this letter we investigate on the use of these latter variables for the description of k-fermions. Namely, we will construct k-fermionic coherent states labeled by Zk-graded Grassmann variables. The coherent states will be used to derive a space of (Zk-graded) Grassmann representatives in which state vectors are represented as ”holomorphic ” functions of the Grassmann variable. There exist many deformations of the harmonic oscillator which, for some values of the deformation parameter, give rise to k-fermions. In this letter we will illustrate the construction using the oscillator deformation of Biedenharn [5] and Macfarlane [6]. This q-oscillator is described by the operators {N, a, a +} with the following relations