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انجمن اپتیک و فوتونیک ایران

Production of a Particular Superposition of Nonlinear Coherent States and Entangled Nonlinear Coherent States

Amir Karimi, Mohammad Kazem Tavassoly

Published Mar 15, 2015• 0 citations
OpenAlex

Abstract

In this paper, after a brief review on the nonlinear coherent states and parity operator by using this operator and nonlinear displacement-type operator, we construct new operators which by the action of them on the vacuum state of the field, we generate a superposition of two nonlinear coherent states and two-modes entangled nonlinear coherent states. Also, we show that by the generalization of the presented method in this paper, the superposition of more than two nonlinear coherent states with the vacuum state of the field and n-mode entangled nonlinear coherent states can be generated.

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In this paper, after a brief review on the nonlinear coherent states and parity operator by using this operator and nonlinear displacement-type operator, we construct new operators which by the action of them on the vacuum state of the field, we generate a superposition of two nonlinear coherent states and two-modes entangled nonlinear coherent states. Also, we show that by the generalization of the presented method in this paper, the superposition of more than two nonlinear coherent states with the vacuum state of the field and n-mode entangled nonlinear coherent states can be generated.
Abstract In this paper, by using the parity operator as well as the nonlinear displacement-type operator, we define new operators which by the action of them on the vacuum state of the radiation field, superposition of two nonlinear coherent states and two-mode entangled nonlinear coherent states are generated. Also, we show that via the generalization of the presented method, the superposition of more than two nonlinear coherent states and n-mode entangled nonlinear coherent states can be generated.
In this paper, after a brief review of the single-mode excited entangled coherent states, two new classes of continuous-variable entangled pure states, namely, single-mode nonlinear excited entangled coherent states, have been produced by using the f -deformed creation operator instead of . In order to establish the nonclassicality of the states, some of the physical properties of the corresponding entangled states, such as entanglement degree, photon statistics, second-order correlation function and quadrature squeezing have been studied in detail by choosing a particular f -deformation function. In addition, the influence of photon excitations on the properties of our introduced states has been analyzed and the results compared with those of a single-mode excited entangled coherent state. In continuation, a theoretical scheme for their generation based on the interaction of a two-level atom with a quantized cavity field has been proposed.
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.
In this paper, after a brief review on the entangled coherent state, a general form of the entangled nonlinear coherent state has been introduced based on the nonlinear coherent states approach. By choosing particular f-deformation functions, theoretical schemes for generation of two distinct classes of such states associated with SU(1,1) and SU(2) groups are presented. The entanglement characteristic of the corresponding entangled coherent states has been studied by evaluating the concurrence. In the continuation, other nonclassical behaviors of the produced states have been analyzed by investigating sub-Poissonian photon statistics, the oscillatory photon number distribution, one- and two-mode quadrature squeezing, and sum and difference squeezing. Accordingly, in addition to their entanglement property, other nonclassicality features of the introduced states are well established in detail.
The main goal of this paper is to present an alternative method to construct new kinds of nonlinear coherent states. To do this, we first establish a class of hypergeometric type of generalized displacement operators, 1 F r ([0], [0, 1, ..., r − 1], za †), act on the vacuum state of the harmonic oscillator and generate normalized quantum states of the Fock space which admit a resolution of the identity through a positive definite measure on the complex plane. Furthermore, realization of the compact form of these states, as functions of the position coordinate x for r = 2, leads to a generating function of the Hermite polynomials in terms of the modified Bessel function. Finally, studying some statistical characters reveals that they have indeed non-classical features such as squeezing, an anti-bunching effect and sub-Poissonian statistics, too.