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Chinese Physics

Three-body entanglement induced by spontaneous emission in a three two-level atoms system

Xiang-Ping Liao, Mao-Fa Fang, Zheng Xiao-Juan, Cai Jian-Wu

Published Jan 16, 2006• 7 citations
Publisher

Abstract

We study three-body entanglement induced by spontaneous emission in a three two-level atoms system by using the entanglement tensor approach. The results show that the amount of entanglement is strongly dependent on the initial state of the system and the species of atoms. The three-body entanglement is the result of the coherent superposition of the two-body entanglements. The larger the two-body entanglement is, the stronger the three-body entanglement is. On the other hand, if there exists a great difference in three two-body entanglement measures, the three-body entanglement is very weak. We also find that the maximum of the two-body entanglement obtained with nonidentical atoms is greater than that obtained with identical atoms via adjusting the difference in atomic frequency.

DOI
10.1088/1009-1963/15/2/021

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We study three-body entanglement induced by spontaneous emission in a three two-level atoms system by using the entanglement tensor approach. The results show that the amount of entanglement is strongly dependent on the initial state of the system and the species of atoms. The three-body entanglement is the result of the coherent superposition of the two-body entanglements. The larger the two-body entanglement is, the stronger the three-body entanglement is. On the other hand, if there exists a great difference in three two-body entanglement measures, the three-body entanglement is very weak. We also find that the maximum of the two-body entanglement obtained with nonidentical atoms is greater than that obtained with identical atoms via adjusting the difference in atomic frequency.
In this paper we consider the situation that four identical two-level atoms are separately trapped in coupled single-mode optical cavities and each atom resonantly interacts with cavity via a one-photon hopping. The three-body entanglement dynamics in each cavity is studied. The influences of atom-cavity coupling constant on the three-body entanglement are discussed. The results obtained using the numerical method show that the three-body entanglement displays the collapse-revival phenomena when atom-cavity coupling constant is larger than a fixed value. On the other hand, the three-body entanglement is the result of the coherent superposition of the two-body entanglements.
After briefly introducing Akhtarshenas, concurrence vector and subvector for describing many-body entanglement, we investigate the entanglement formation for a system which contains three bodies, i.e. two identical atoms and a single-model cavity field, in the Tavis–Cummings model by calculating the concurrences. The results show that the coupling strength between two atoms, the decay cavity and the atomic spontaneous emission can change the entanglement of formation according to different modes: these factors destroy periodicity and symmetry of all concurrences, and that the coupling strength of two atoms does not change the peak value of concurrence ( C ), but the strength of decay cavity and the atomic spontaneous emission decline in the peak value of concurrence ( C ) and the latter is more serious than the former under the same strengths. The concurrence vector and subvector are a useful measure of entanglement for a pure state of the many-body system, in that it can give novel pictures about the entanglements for the entire system and between its inner bodies.
Abstract. We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulas for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r12 and interact with each other via the dipole-dipole interaction, and the antisymmetric state of the system is included throughout, even for small inter-atomic separations, in contrast to the small sample model. It is shown that for sufficiently large values of the dipole-dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.
We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulae for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r 12 and interact with each other via the dipole–dipole interaction, and the antisymmetric state of the system is included throughout, even for small interatomic separations, in contrast to the small-sample model. It is shown that for sufficiently large values of the dipole–dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.
The case that one of the two entangled identical two-level atoms interacts with a single-mode field among three-body entanglement was mainly considered. The results show that in initial the more the degree of entanglement of the two entangled atoms have, the more oscillation of the entanglement measure will have,and the more times of the maximally entanglement measure will obtain. Meanwhile, it was found that entanglement measure will be reduced when atomic coupling coefficient is larger than coupling coefficient between field and atom.
The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.