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Results in Physics

Optical tomography for excited coherent states associated to deformed oscillators

Abdullah M. Almarashi, Ali Algarni, Fahad M. Al-Aboud, S. Abdel‐Khalek, K. Berrada

Published Jun 7, 2019• 5 citations
Publisher

Abstract

In this manuscript, we study the deformed optical tomography for excited coherent states associated to deformed Heisenberg algebra. By using the numerical solution of the recurrence relation, we evaluate the eigenstates of the deformed quadrature operator and give the exact analytical formula of the optical tomogram for the photon-added deformed coherent states (PA-DCSs) and photon-added deformed cat coherent states (PA-DCCSs). Finally, we display the variation of the excited coherent states in the terms of the different physical parameters defined in the coherent states and show how these parameters affect the shape of the optimal tomography.

DOI
10.1016/j.rinp.2019.102352

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In this manuscript, we study the deformed optical tomography for excited coherent states associated to deformed Heisenberg algebra. By using the numerical solution of the recurrence relation, we evaluate the eigenstates of the deformed quadrature operator and give the exact analytical formula of the optical tomogram for the photon-added deformed coherent states (PA-DCSs) and photon-added deformed cat coherent states (PA-DCCSs). Finally, we display the variation of the excited coherent states in the terms of the different physical parameters defined in the coherent states and show how these parameters affect the shape of the optimal tomography.
We introduce entangled pair coherent states of a noncommutative harmonic oscillator operators associated with a q-deformed oscillator algebra. The definition of two-mode q-deformed operator and the decomposition of its eigenstates in terms of the q-deformed Fock states are obtained. The general solution of the recurrence relation of the first nondeformed quadrature is obtained. The asymptotic behavior of the general solution is studied, a complete expansion is derived, and also representations of the general solution in terms of the Gauss hypergeometric function are given. Also, we prove that the general solution is related to Meixner-Pollaczek orthogonal polynomial and calculate the weight function. The photons number distribution, the second order correlation function and the optical tomogram of the entangled pair coherent states are discussed. The recurrence relation for the first q-deformed quadrature is inferred. We evaluate the eigenstate of the q-deformed quadrature operator and give a numerical study for the optical tomogram of the q-deformed of the entangled pair coherent states. Finally, we show the change of the parameters in the entangled pair coherent states that connected with physical quantities and explain how they affect the format of optimal tomography.
In the present article, we build the excitedcoherent states associated with deformed su(1,1) algebra (DSUA), called photon-added deformed Perelomov coherent states (PA-DPCSs). The constructed coherent states are obtained by using an alterationof the Holstein–Primakoff realization (HPR) for DSUA. A general method to resolve of the problem of the unitary operator was developed for these kinds of quantum states. The Mandel parameter is considered to examine the statistical properties of PA-DPCSs. Furthermore, we offer a physical method to generate the PA-DPCSs in the framework of interaction among fields and atoms. Finally, we introduce the concept of entangled states for PA-DPCSs and examine the entanglement properties for entangled PA-DPCSs.
By introducing a generalization of the (p, q)-deformed boson oscillator algebra, we establish a two-parameter deformed oscillator algebra in an infinite-dimensional subspace of the Hilbert space of a harmonic oscillator without first finite Fock states. We construct the associated coherent states, which can be interpreted as photon-added deformed states. In addition to the mathematical characteristics, the quantum statistical properties of these states are discussed in detail analytically and numerically in the context of conventional as well as deformed quantum optics. Particularly, we find that for conventional (nondeformed) photons the states may be quadrature squeezed in both cases Q = pq < 1, Q = pq > 1 and their photon number statistics exhibits a transition from sub-Poissonian to super-Poissonian for Q < 1 whereas for Q > 1 they are always sub-Poissonian. On the other hand, for deformed photons, the states are sub-Poissonian for Q > 1 and no quadrature squeezing occurs while for Q < 1 they show super-Poissonian behavior and there is a simultaneous squeezing in both field quadratures.PACS Nos.: 42.50.Ar, 03.65.–w
Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.
In present manuscript, we build the photon-added deformed spin coherent states (PA-DSCSs) according to deformed spin algebra (DSA). We present the way for solving the unity operator problem and we give the solution for some particular cases. The obtained states are developed through the Holstein-Primakoff (HP) realization of the DSA. The statistical features of the obtained coherent states are examined through the variation of the Mandel’s parameter. By using the PA-DSCSs, we investigate the bipartite entanglement with respect to different parameters of these states.
We construct deformed photon-added nonlinear coherent states (DPANCSs) by application of the deformed creation operator upon the nonlinear coherent states obtained as eigenstates of the deformed annihilation operator and by application of a deformed displacement operator upon the vacuum state. We evaluate some statistical properties like the Mandel parameter, Husimi, and Wigner functions for these states and analyze their differences; we give closed analytical expressions for them. We found a profound difference in the statistical properties of the DPANCSs obtained from the two abovementioned generalizations.