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Chinese Physics B

Formation of three-body entanglement via a vacuum optical cavity induction in Tavis–Cummings model

Yuliang Li, Xuemei Li

Published Mar 1, 2008• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/17/3/013

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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.
After briefly introducing Akhtarshenas,concurrence vector and subvector to describe many-body entanglement,we have investigated the entangled formation of the system which contains three bodies——two identical atoms and a single-model cavity field in Tavis-Cummings model by calculating the concurrences.The results show that the total concurrence vector C and subvector C{ij} change periodically and show themselves symmetrically when the initial state of the system is separable,all concurrence is insensitive to the initial states of two atoms as increasing photons of cavity field and description of a refreshing structure about entanglement of formation in the entire system and between its inner bodies.
This paper studies the quantum entanglement of the Tavis-Cummings model for two steady identical two-level atoms interac-ting with a single-mode field. Whe n the field is vacuum and the two atoms stay in Einstein-Podolsky-Rosem entangle d state or disentangled state initially, we obtain that the system will evol ve to a three-body approximate W entangled state. The entanglement measure will change with the variation of system initial state, coupling coefficients, detuni ng degree and atomic population inversion. It should be noted that the atomic co upling coefficient exhibits the nonlinear effect and the entanglement measure os cillates periodically in accordance with atomic population inversion.
The quantum entanglement of the Tavis-Cummings model for two identical two-level atoms interacting with a single-mode field is considered.When the field is one photon and the two atoms stay in ground states initially,it is abtained that the system will evolve to a three-body approximate state.The result shows that every entanglement measure of the system will be reduced when atomic coupling coefficient is larger than coupling coefficient between field and atom,and the entanglement measure of atoms and the entanglement measure between two atoms with field will be reduced more quickly.Meanwhile,every entanglement measure periodic will be also shortened relevantly.
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.
This paper investigates quantum entanglement of two atoms in the non-dissipative and dissipative cases by means of concurrence.The results indicate that maximum entanglement condition can be prepared by controlling the interacting time and due to the two-photon transition of atoms,the time required to prepare the maximum entanglement in two-photon Tavies-Cummings model is of that in single-photon Tavies-Cummings model.In addition,the atomic spontaneous emission and cavity decay make the maximum coherence of two atoms decrease periodically.
The three-qubit entangled state in Tavis-Cummings model for two identically steady two-level atoms interacting with single mode field can be generated when the atom-field interaction is far from atom-atom interaction.By analyzing three-qubit entanglement of the system,we obtain that the entanglement of the system will change with the variation of system initial state,coupling coefficients between atom and field or atoms.Especially,when the initial state is special,the system will stay in W-entangled state.The necessary condition for generating W-state is that the coupling constant between two atoms is more less than that of between an atom and field.