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Physica Scripta

Wehrl entropy and Wehrl phase distribution of a single-trapped ion interacting with a laser field

S. Abdel‐Khalek

Published Sep 15, 2009• 29 citations
Publisher

Abstract

In this paper, some properties of the interaction between a single-trapped ion and laser fields are discussed. Analytical and explicit expressions of the Wehrl entropy and Wehrl phase distribution are given taking into account different configurations of the laser field. The results show the important roles played by the fluctuations of the laser phase and initial state setting in the evolution of the Husimi Q -function, Wehrl entropy and Wehrl phase distribution.

DOI
10.1088/0031-8949/80/04/045302

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In this paper, some properties of the interaction between a single-trapped ion and laser fields are discussed. Analytical and explicit expressions of the Wehrl entropy and Wehrl phase distribution are given taking into account different configurations of the laser field. The results show the important roles played by the fluctuations of the laser phase and initial state setting in the evolution of the Husimi Q -function, Wehrl entropy and Wehrl phase distribution.
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.
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.
This contribution explores the perceptions, ideas and understanding about the phase entropy of the ion-field interaction. Here we discuss the interaction between a single qubit (trapped ion) and a single laser field. We construct the explicit solution of this problem. Employing an obtained exact solution of the problem, significant features of the phase entropy in the context of the measure defined by phase probability distribution are observed. We discuss the relationship between entropic uncertainty relations and entanglement. Implications of the results for different physical parameters are discussed.
The Wehrl phase distribution is defined as a phase density of the Wehrl classical information entropy. The new measure is applied to describe the quantum phase properties of some optical fields including Fock states, coherent and squeezed states, and superposition of chaotic and coherent fields. The Wehrl phase distribution is compared with both the conventional Wehrl entropy and Husimi phase distribution (the marginal Husimi Q -function). It is shown that the Wehrl phase distribution is a good measure of the phase-space uncertainty (noise), phase locking and phase bifurcation effects. It is also demonstrated that the Wehrl phase distribution properly describes phase randomization processes, and thus can be used in a description of the quantum optical phase.
The laser field interacting with single trapped ion in a carrier excitation frame in the presence of an external field is investigated. Detailed analytical expressions are given, taking into account carrier excitation configurations. We study the evolution of the population inversion, fidelity, ion-field entanglement, Fisher information and the geometric phase. The results indicate the influence of the external field on the information quantities to describe some physical phenomena. The relation between the population inversion, fidelity, von Neumann entropy, Fisher information, and geometric phase are explored during the time evolution.