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Laser Physics Letters

Entanglement of a bipartite mixed state in the laser-ion interaction with a binomial state

Mahmoud Abdel‐Aty

Published Jan 20, 2004• 7 citations
Publisher

Abstract

In the present communication we explore and develop the theory of entanglement measures. As a result we obtain a general criterion of a bipartite mixed states entanglement due to the quasi-mutual entropy for a single trapped two-level ion interacting with a laser field. This general expression of the entanglement degree is obtained with the physical significance and without the diagonal approximation. We indicate how the entanglement affected by different values of the Lamb-Dicke parameter of the initially generalized binomial state. Among the new features found, it is shown, for the large number of quanta, that the shape of entanglement could oscillate around the maximum value, which is related to the existence of a strong entanglement in the present system.

DOI
10.1002/lapl.200310029

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In the present communication we explore and develop the theory of entanglement measures. As a result we obtain a general criterion of a bipartite mixed states entanglement due to the quasi-mutual entropy for a single trapped two-level ion interacting with a laser field. This general expression of the entanglement degree is obtained with the physical significance and without the diagonal approximation. We indicate how the entanglement affected by different values of the Lamb-Dicke parameter of the initially generalized binomial state. Among the new features found, it is shown, for the large number of quanta, that the shape of entanglement could oscillate around the maximum value, which is related to the existence of a strong entanglement in the present system.
In this paper we use the quasi-mutual entropy, which does not depend on quantum channel, as a measure of information content of ionic state due to ion-laser interaction in a single trapped ion. It is found that the quasi-mutual entropy is a good measure of the entanglement degree of the ionic state at any time. We examine numerically the population inversion, the photon number distribution and degree of entanglement due to quasi-mutual entropy for a single trapped ion interacting with a laser held. During the transition from collapse to revival and vice-versa we have a minimum degree of entanglement value. Successive revival peaks show a lowering of the local maximum points indicating a dissipative irreversible change in the ionic state. We propose a generation of Bell-type states having a simple initial state preparation of a single trapped ion.
In this study, our goal is to obtain the entanglement dynamics of trapped three-level ion interaction two laser beams in beyond Lamb-Dicke parameters. Three values of LDP, η=0.09, η=0.2 and η=0.3 are given. We used the concurrence and the negativity to measure the amount of quantum entanglement created in the system. The interacting trapped ion led to the formation of phonons as a result of the coupling. In two quantum systems (ion-phonons), analytical formulas describing both these measurements are constructed. These formulas and probability coefficients include first order terms of final state vector. We report that long survival time of entanglement can be provided with two quantum measures. Negativity and concurrence maximum values are obtained N = 0.553 and for LDP = 0.3. As a similar, the other two values of LDP are determined and taken into account throughout this paper. For a more detailed understanding of entanglement measurement results, “contour plot” was preferred in Mathematica 8.
In this communication, the entanglement degree due to quasi-mutual entropy of a three-level atom interacting with a single cavity field is investigated. We consider the situation for which the three-level system is initially in a mixed state, whereas the field may start from either a coherent or a squeezed state. We present a derivation of the unitary evolution operator on the basis of the dressed-state formalism taking into account an arbitrary form of nonlinearity of the intensity-dependent coupling, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the degree of entanglement are influenced significantly by different forms of the nonlinearity. The atom and radiation subsystems exhibit alternating sets of collapses and revivals due to the initially mixed states of the atom and radiation employed here.
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 time evolution properties of the field quantum entropy in the system of a trapped ion interacting resonantly with a standing-wave laser field is studied by utilizing the Von Neumann reduced quantum entropy theory, and our attention focuses on the discussion of the influence of the Lamb-Dick parameter, the position of the ion in the standing-wave laser field and the initial state of the trapped ion on the evolution properties of the field quantum entropy. The results obtained from the numerical calculation indicate that: the value of the Lamb-Dick parameter effect the oscillation frequency and amplitude of the quantum entanglement between the trapped ion and the standing-wave laser field, the larger the Lamb-Dick parameter is, the weaker the average entanglement level between the ion and the field will be. When moving the tapped ion from the node of the standing-wave laser to the loop, the vibration frequency of the quantum entanglement between the field and the ion becomes slow gradually, and the entanglement degree gets weaker and weaker. With the decrease of the probability of the trapped ion being in the excited state, the quantum entanglement between the trapped ion and the stanging-wave laser field shows the tendency of increase first and then decrease. These properties have certain reference value for the preparation of entangled states and for the quantum communications with the thapped ion, and so on.
A quantum scheme is presented by which a three-level trapped ion interacts with a two laser beams in the absence and presence of the e®ect of classical field. We analyze the impact of the classical ¯eld and the Lamb-Dicke parameter (LDP) on the dynamical behavior of entanglement quanti¯er, population probabilities and the geometric phase. Based on four different variations of these two effects, LDP = 0.1, LDP=0.01 and ¯ = 0.0, ¯ = 0.49, the time dependence of geometric phase and populations probabilities are shown. The ¯nding emphasizes that both the time-dependent and LDP play an important role in the development of the entanglement, the geometric phase, ¯delity, and populations probabilities. This in-sight may be very useful in various applications in quantum optics and information processing.