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Results in Physics

Photon-added deformed spin coherent states and bipartite entanglement

K. Berrada, A. Sabik, Hichem Eleuch

Published Jul 10, 2023• 1 citation
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2023.106705

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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.
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.
In the present work, we construct and investigate some properties of the photon-added spin coherent states (PA-SCSs). The Klauder’s minimal set of conditions required to obtain coherent states are discussed. We give the analytical form for the positive weight function in the resolution of unity. Finally, we examine the statistical properties of the PA-SCSs in terms of different parameters using the Mandel’s Q-parameter. All these quantities are expressed in terms of hypergeometric and Meijer G-functions, and so, the PA-SCSs are a new field of application for these functions.
In this paper, we introduce the parity extension of the harmonic oscillator systems to develop the generalized Tavis-Cummings model (T-CM) based on a specific deformation of the Heisenberg algebra. We present a quantum scheme of a two-qubit system (TQS) interacting with a quantized field that is initially prepared in parity deformed coherent states (PDCSs). The dynamical features of the considered system are explored in the presence of parity deformed parameter (PDP) and time-dependent coupling (t-dc). In particular, we examine the amount of the entanglement formed in the qubit–field and qubit–qubit states. We find that the maximal amount of the entanglement may be occurred periodically during the time evolution. Finally, we investigate the influence of PDP on the Fisher information and the photon statistics of the deformed field with respect to the main parameters of the system.
In this paper, we construct photon-added f -deformed coherent states (PA f -DCSs) for nonlinear bosonic fields by discussing Klauder's minimal set of conditions required to obtain coherent states. Using this set of nonlinear states, we propose a very useful scheme for generating the maximal amount of entanglement via unitary beam splitters for different strength regimes of the input field α, deformation q and excitation number m . Therefore, the possibility to create highly entangled states and to control the entanglement is proposed. Moreover, the condition for a maximal and separable output beam state is obtained. Finally, we examine the statistical properties of the PA f -DCSs through the Mandel parameter and exploit a connection between this quantity and the behavior variation of the output state entanglement. Our result may open new perspectives in different tasks of quantum information processing.
In this paper, we will try to present a general formalism for the construction of deformed photon-added nonlinear coherent states (DPANCSs) |α, f , m ⟩, which in a special case lead to the well-known photon-added coherent state (PACS) |α, m ⟩. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that the introduced states can also be classified in the f -deformed coherent states, with a special nonlinearity function. Next, we will show that these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of m , i.e. |α, f , − m ⟩, is then presented. Our approach has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, non-degenerate spectrum. Finally, after applying the formalism to a particular physical system known as the Pöschl–Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function , some of the non-classical properties, such as the Mandel parameter, second-order correlation function, in addition to first- and second-order squeezing of the corresponding states, will be investigated numerically.
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.