S. Abdel-Khalek

Geometric phase of a moving three-level atom

Abstract In this paper, we investigate the geometric phase of the field interacting with Ξ -type moving three-level atom. The results show that the atomic motion and the field mode structure play an important roles in the evolution of the system dynamics and geometric phase. We test this observation with experimentally accessible parameters and some new aspects are obtained.

Beam splitter entangler for nonlinear bosonic fields

Some years ago Katriel and Solomon [1] described applications to the characterization of the photon statistics of nonideal lasers, nonclassical light, and deformed photon states using f-deformed coherent states. In this letter, we study the effect of a beam splitter on these nonlinear coherent states. We find that these states are useful for generating quantum entanglement as the deformation parameter gets farther form the unity and for strong input field regimes. The results are confirmed through the Werhl entropy.

Entanglement of a two-level atom papered in a finite trio-coherent state

In this paper, we study the interaction between an effective two-level atom and a three-mode field. The atom and the field are initially in the excited state and finite dimensional trio-coherent state, respectively. For this sytem, we investigate the atomic inversion, the von Neumann entropy, and the atomic Wehrl entropy. We show that there is a connection between all of these quantities. Also, we prove that the atomic Wehrl entropy exhibits a temporal evolution similar to the von Neumann entropy. It is observed that the Stark shift parameter plays an important role on the evolution of these quantities.

Geometric phase and entanglement for a single qubit interacting with deformed-states superposition

The geometric phase and quantum entanglement for a nonlinear field-atom system are described quantitatively in terms of different parameters. Specifically, considering a deformed Schrödinger cat interacting with a qubit and taking into account the time dependent of the system coupling. The results show that the initial state setting, atomic motion, photon number and deformation play important roles in the evolution of the system dynamics, nonlocal correlation and geometric phase. An interesting correlation between the entanglement and geometric phase is observed during the time evolution. The presented system is very useful to generate and maintain high amount of entanglement through controlling the phase variation of the system under consideration. We test this observation with experimentally accessible parameters and some new aspects are obtained.

Nonlocal correlations for manifold quantum systems: Entanglement of two-spin states

In this paper, we study the bipartite entanglement of spin coherent states in the case of pure and mixed states. By a proper choice of the subsystem spins, the entanglement for large class of quantum systems is investigated. We generalize the result to the case of bipartite mixed states using a simplified expression of concurrence in Wootters’ measure of the bipartite entanglement. It is found that in some cases, the maximal entanglement of mixed states in the context of su(2) algebra can be detected. Our observations may have important implications in exploiting these states in quantum information theory.

Atomic Wehrl Entropy of a Single Qubit System

We propose the use of atomic Wehrl entropy associated to the reduced atomic density operator as an entanglement indicator of bipartite systems. This is applied to a two-level system (one single harmonically trapped ion) by taking into account the linear center-of-mass-motional degree of freedom. Detailed analytical and explicit expressions are given, taking into account different configurations. The results show the important roles played by the laser phase and initial state setting in the evolution of the atomic Q-function, atomic Wehrl entropy and marginal atomic Q-function. Our procedure of using atomic Wehrl entropy may be applied to a system with Hilbert space of high dimension.

Interplay of information quantifiers and the modified Jaynes-Cummings model

The dynamics of the Buck and Sukumar model (B. Buck and C. V. Sukumar, Phys. Lett. A 81, 132 (1981)) is investigated using different semi-classical information-theory tools. Their interplay reveals somewhat unexpected features. A new signature for the classical-quantum barrier is encountered thereby.

Measures of nonclassicality for a two-level atom interacting with power-law potential field under decoherence effect

In this paper, we propose a useful quantum system to perform different tasks of quantum information and computational technologies. We explore the required optimal conditions for this system that are feasible with real experimental realization. We present an active way to control the variation of some measures of nonclassicality considering the time-dependent coupling and photon transition effects under a model that closely describes a realistic experimental scenario. We investigate qualitatively the quantum measures for a two-level atom system interacting with a quantum field initially defined in a coherent state in the framework of power-law potentials (PLPCSs). We study the nonlocal correlation in the whole system state using the negativity as a measure of entanglement in terms of the exponent parameter, number of photon transition, and phase damping effect. The influences of the different physical parameters on the statistical properties and purity of the field are also demonstrated during the time evolution. The results indicate that the preservation and enhancement of entanglement greatly benefit from the combination of the choice of the physical parameters. Finally, we explore an interesting relationship between the different quantum measures of non-classicality during the time evolution in the absence and presence of time-dependent coupling effect.

Geometric phase and entanglement of Raman photon pairs in the presence of photonic band gap

Robustness of the geometric phase (GP) with respect to different noise effects is a basic condition for an effective quantum computation. Here, we propose a useful quantum system with real physical parameters by studying the GP of a pair of Stokes and anti-Stokes photons, involving Raman emission processes with and without photonic band gap (PBG) effect. We show that the properties of GP are very sensitive to the change of the Rabi frequency and time, exhibiting collapse phenomenon as the time becomes significantly large. The system allows us to obtain a state which remains with zero GP for longer times. This result plays a significant role to enhance the stabilization and control of the system dynamics. Finally, we investigate the nonlocal correlation (entanglement) between the pair photons by taking into account the effect of different parameters. An interesting correlation between the GP and entanglement is observed showing that the PBG stabilizes the fluctuations in the system and makes the entanglement more robust against the change of time and frequency.

WEHRL ENTROPY AND ENTANGLEMENT OF A TIME-DEPENDENT TWO-LEVEL TRAPPED ION INTERACTING WITH A LASER FIELD

The time evolution of the atomic Wehrl entropy and long-lived entanglement generation using a single trapped ion interacting with a laser field are analyzed. Starting from the Heisenberg equation of motion, an exact solution of the system is obtained by indicating that there are some interesting features when a time-dependent modulating function is considered. We demonstrate that the long-living quantum entanglement can be obtained using the time-independent interaction when the field is initially in a pair cat states.