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Chinese Physics B

Entanglement properties between two atoms in the binomial optical field interacting with two entangled atoms

Tang-Kun Liu, Kang-Long Zhang, Yu Tao, Chuan-Jia Shan, Ji-Bing Liu

Published Jul 1, 2016• 4 citations
Publisher

Abstract

The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.

DOI
10.1088/1674-1056/25/7/070304

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The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.
In this article, the dynamical properties in the system of two identical twolevel entangled atoms interacting with a binomial optical field are studied by means of time evolution operator and numerical calculations. The results show that the time evolution of atomic population and atomic dipole squeezing depends on the degree of entanglement of the initial two identical twolevel entangled atoms and the parameters of the binomial state optical field. The atomic dipole moment can be completely squeezed via choosing appropriate parameters of the system.
The entanglement character of two entangled atoms interacting with the binomial light-field in a multiphoton Tavis-Cumming model(T-C model) is studied by means of the quantum theory.The influences of the optical field parameters and the atomic dipole-dipole coupling intensity of the atoms on the properties of the entanglement between two atoms under different initial states are discussed.The results indicate that the periodicity of the entanglement between two atoms is influenced by the parameters of the binomial optical field.There are the entanglement phenomena at some values of nπ except the value of 5nπ(n=0,1,2,…).With the increase of the parameters of the binomial optical field,the range appearing entanglement phenomenon will increase gradually.Thereby the time in that the entanglement between the two atoms occurs will diminish.The atomic dipole-dipole coupling intensity has an effect on oscillating of entanglement and the entanglement degree between the two atoms.
The field entropy evolution of two moving atoms interacting with the binomial field in Tavis-Cummings model is studied by means of the quantum theory.The influences of atomic motion and the parameters of the binomial optical field under different initial states are discussed emphatically.With the increase of the parameters of the binomial optical field,the entanglement degree between field and atoms is strengthened firstly and is weakened later.When the field is in the middle states,And as the speed of the moving atoms increases,the atom-field system will stay in the maximum entangled state.the entanglement degree between the field and atoms is weaken and the periodicity of the evolution of the field entropy decreased.When the field is in the middle states and the atoms is at the lower speed,the entanglement between the binomial field and the two atoms can be kept for much longer time.
By means of the quantum theory and the method of the negative eigenvalues of the partial transposition,the properties of entanglement evolution in the system of two two-level atoms coupled to a light field in the binomial state for radiation field are investigated in the presence of phase decoherence in the multiphoton Tavis-Cumming Model.The influences of the maximum number of photons,the coefficient of binomial state for radiation field,the phase decoherence coefficient and the number of the transitional photons on the entanglement degree between two atoms have been discussed.The results show that the entanglement between two atoms will get steady state more easily,and the steady value of the entanglement degree is bigger than before with the increase of the maximum number of photons in the presence of phase decoherence.The entanglement between two atoms will approach a steady state more easily.The steady value will be diminished with the increase of the coefficient of binomial state for radiation field in selecting the proper parameter.The periods of the entanglement evolution are more obvious when the coefficient η of binomial state for radiation field is smaller.The entanglement evolution does not have the periodicity and tends the disentanglement phenomenon easily with the increase of the phase decoherence coefficient.The periods of the entanglement evolution is shorten and the entanglement intensity is weaken with the increase of the number of the transitional photons.
Using negative entropy method,the quantum entanglement characteristics of the system of binomial optical field interacting with moving atom were studied.The influences of the atomic initial state,field-mode structure parameter,maximum photon number of binomial field,coefficient of binomial field,transition photon number and detuning were discussed.The results show that the value of entanglement degree of the system appears regular evolution and entanglement sudden death(ESD) phenomenon when atomic motion was considered.The increasing of the field-mode structure parameter shortens the period of the entanglement and results in a slight decreasing of amplitude.The atomic initial state affects the entanglement degree of the system.When the atomic initial state tends to pure state,the entanglement degree of the system is larger relatively.With increase of the maximum photon number of binomial field,the value of the entanglement degree of system becomes small,but the period for regular evolution is almost unchanged.When the field is in the middle states,the entanglement degree is smaller relatively.With the increase of the transition photon number,the value of the entanglement degree of the system becomes larger,the period of the oscillation becomes shorter,meanwhile the oscillation of the system becomes faster and faster.With the detuning increasing,the entanglement becomes small.