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انجمن اپتیک و فوتونیک ایران

Nonlinear Displaced Number States and Their Non-classical Properties

N. Asili Firouzabadi, Mohammad Kazem Tavassoly

Published Feb 15, 2014• 0 citations
OpenAlex

Abstract

In this paper, we intend to introduce a particular class of radiation field which is called nonlinear displaced number states. Then we will investigate a few of their non-classical properties, like sub-Poissonian statistics, quadratuer squeezing, amplitude-squared squeezing, Husimi and Wigner quasi-distribution functions.

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Abstract Since radiation field states are very important in the interaction with the various atomic structures, in this article we introduce a new type of quantum states, which we call ‘Mth nonlinear coherent states’. We define these states based on acting of the number operator M times n ˆ M on a nonlinear coherent state. By analyzing the photon distribution function and its overlap with the nonlinear coherent states, it becomes clear that these states are very similar to the corresponding nonlinear coherent states. We also investigate the nonclassical features of such states for different values of M, and it is determined that the occurrence of sub-Poissonian photon statistics, normal squeezing, and amplitude squared squeezing are considerable nonclassical properties of the Mth nonlinear coherent states. Also, examining the Husimi function shows a local behavior for the introduced states. Furthermore, by calculating the Wigner function, we find out that in some points of the phase space, the value of this function is negative which could be considered as a nonclassical feature for these states.
Recently, nonlinear displaced number states (NDNSs) have been manually introduced, in which the deformation function f ( n ) has been artificially added to the previously well-known displaced number states (DNSs). Indeed, just a simple comparison has been performed between the standard coherent state and nonlinear coherent state for the formation of NDNSs. In the present paper, after expressing enough physical motivation of our procedure, four distinct classes of NDNSs are presented by applying algebraic and group treatments. To achieve this purpose, by considering the DNSs and recalling the nonlinear coherent states formalism, the NDNSs are logically defined through an algebraic consideration. In addition, by using a particular class of Gilmore–Perelomov-type of SU (1, 1) and a class of SU (2) coherent states, the NDNSs are introduced via group-theoretical approach. Then, in order to examine the nonclassical behavior of these states, sub-Poissonian statistics by evaluating Mandel parameter and Wigner quasi-probability distribution function associated with the obtained NDNSs are discussed, in detail.
We construct a distinct class of nonlinear displaced Kerr states by application of the displacement operator upon a state which is prepared by sending the well-known photon-added coherent state through a normal Kerr medium. A sketch for the experimental setup for preparing the state is suggested. We evaluate some statistical properties such as the photon number distribution, Mandel’s Q parameter, Husimi-Q and Wigner functions, and quadrature squeezing for the nonlinear displaced Kerr state and then analyze the nonclassicality in terms of these standard parameters. We reduce the infinite-level problem to a truncated discrete two-level system by using a low Kerr parameter approximation and then convert the generated nonclassicality into bipartite entanglement between the two modes of an output state of a linear optical device.
We construct nonlinear squeezed states of a generalized isotonic oscillator potential. We demonstrate the non-existence of a dual counterpart of nonlinear squeezed states in this system. We investigate the statistical properties exhibited by the squeezed states, in particular Mandel's parameter, second-order correlation function, photon number distributions and parameter A 3 in detail. We also examine the quadrature and amplitude-squared squeezing effects. Finally, we derive the expression for the s -parameterized quasi-probability distribution function of these states. All this information about the system is new to the literature.