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arXiv:1202.4583 · Journal of Physics A Mathematical and Theoretical

A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator

V. Chithiika Ruby, Murugaian Senthilvelan

Published Mar 5, 2012• 3 citations
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Abstract

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.

DOI
10.1088/1751-8113/45/12/125302

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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.
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We explore squeezed coherent states of a three-dimensional generalized isotonic oscillator whose radial part is the newly introduced generalized isotonic oscillator whose bound state solutions have been shown to admit the recently discovered X 1 -Laguerre polynomials. We construct a complete set of squeezed coherent states of this oscillator by exploring the squeezed coherent states of the radial part and combining the latter with the squeezed coherent states of the angular part. We also prove that the three-mode squeezed coherent states resolve the identity operator. We evaluate Mandel’s Q -parameter of the obtained states and demonstrate that these states exhibit sub-Possionian and super-Possionian photon statistics. Furthermore, we illustrate the squeezing properties of these states, both in the radial and angular parts, by choosing appropriate observables in the respective parts. We also evaluate the Wigner function of these three-mode squeezed coherent states and demonstrate the squeezing property explicitly.
Abstract We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients z n / n ! zn/n!{z}^{n}/\sqrt{n!}zn/n!​ of the canonical coherent states by the factorial x n γ ! = x 1 γ . x 2 γ … x n γ xnγ!=x1γ.x2γ…xnγ{x}_{n}^{\gamma }!={x}_{1}^{\gamma }.{x}_{2}^{\gamma }\dots {x}_{n}^{\gamma }xnγ​!=x1γ​.x2γ​…xnγ​ with x 0 γ = 0 x0γ=0{x}_{0}^{\gamma }=0x0γ​=0 , where x n γ xnγ{x}_{n}^{\gamma }xnγ​ is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.
In this paper, we introduce two new classes of nonlinear squeezed states that we name as f-deformed squeezed vacuum state |ξ, f〉 even and f-deformed squeezed first excited state |ξ, f〉 odd , which according to their production processes, essentially include only even and odd bases of Fock space, respectively. In the continuation, we introduce the superposition of these two distinct nonlinear squeezed states with a respective phase φ. Then, some of the criteria which imply the nonclassicality of the states, such as Mandel parameter, second-order correlation function, quadrature squeezing, amplitude-squared squeezing, Husimi and Wigner–Weyl quasi-distribution functions, are numerically examined. At last, by considering a well-known nonlinearity function associated with a nonlinear physical system, we present our results which outcome from the numerical calculations. It is shown that, the introduced f-deformed states can reveal high nonclassical features.
Abstract Two-mode nonlinear semi-coherent states and their even and odd superpositions are defined. Their non-classical properties, including photon statistics and squeezing, are then evaluated. We use the Mandel parameter and the second-order coherence function to study sub-Poissonian photon statistics and the photon antibunching effect. By calculating the variance of two-mode quadrature operators, we evaluate the squeezing effect for the introduced states. Next, we examine entanglement using concurrence. We have found that all states display non-classical properties within certain ranges of the parameters involved. The calculation of concurrence demonstrates that all states are entangled within specific ranges of parameters.