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Journal of Minjiang University

Concurrence vectors and description of entangled formation for a three-body system

Yuliang Li

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
In this paper we consider the situation that three identical two-level atoms resonantly interact with three distant single-mode optical cavities via a one-photon hopping separately.Three atoms are in like-GHz state and therr optical cavities are all in vacuum state initially.Using the Jaynes-Cummings,the time evolution of the system is given.We adopt the entanglement tensor approach to quantify the degree of entanglement.The tripartite entanglement dynamics among three atoms and the entanglement dynamics between two atoms are studied.The influence of atomic states initially on tripartite entanglement among atoms and two-body entanglement between two atoms are discussed.The results obtained using the numerical method show:first,the time evolution of tripartite entanglement displays the periodic oscillation behavior and its oscillation period is not realted with the initial degree of entanglement among atmos;second the peak and mean of entanglement measures E3 and F2 incease with increasing of the initial degree of entanglement among atmos,which means that the larger the initial degree of entanglement among atoms,the layer the tripartite entanglement among atoms and the two-body entanglement between atoms;third,the phenomenon of sudden death of entanglement between two atoms occurs,and the length of the death time interval decreases with increasing of the initial degree of entanglement among atoms.This shows that the length of the death time interval of two-body entanglement can be decreased by selecting initially atomic state with high degree of entanglement among atoms.
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.
In light of quantum theory,we investigate the entanglement properties of two entangled two-level atoms that interact resonantly with a single-mode vacuum field with atomic motion.The results show that if the two atoms are prepared in maximun entangled(EPR)state initially,the maximum of three-body entanglement measure is equated with the perfect three-body W entangled state.The parameter of field-mode structure p influences the time evolution osciuation property of three-body entlinglement measure,with the gradually increasing of p,the average of three-body entanglement measure will gradually decrease,three-body entangled state will tend to disentangled state inch by inch.