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ACTA PHOTONICA SINICA

Quantum Entanglement of the Coherent State Field Interacting with a Λ Type Three-level Atom Without Rotating Wave Approximation

夏建平 XIA Jian-ping, 任学藻 Ren Xuezao, 丛红璐 Cong Honglu, 姜道来 JIANG Dao-lai, 廖旭 Liao Xu

Published Jan 1, 2010• 1 citation
Publisher

Abstract

Applying the method of coherent-state orthogonalization expansion, the quantum entropy of the coherent state light field interacting with a Λ type three level atom is caculated accurately without rotating wave approximation. The influences of the couplings, mean photon number and the atom in different levels at the initial time on quantum entanglement are studied via quantum entropy theory. The results obtained from using the numerical method show that when atom is initially in the excited state, the entanglement reaches the maximum value in a short time, with the increase of the mean photon number, the period of entanglement evolution becomes clearly. The degrees of enganglement in a short time become lower due to the atom is initially in the superposition state of all three levels. Compared with the results of using the method of rotating wave approximation, the contribution of the without rotating wave approximation terms increase notably and the quantum entanglement curvies displays small zigzag-shaped oscillation, with the increasing of couplings and mean photon number.

DOI
10.3788/gzxb20103909.1621

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Applying the method of coherent-state orthogonalization expansion, the quantum entropy of the coherent state light field interacting with a Λ type three level atom is caculated accurately without rotating wave approximation. The influences of the couplings, mean photon number and the atom in different levels at the initial time on quantum entanglement are studied via quantum entropy theory. The results obtained from using the numerical method show that when atom is initially in the excited state, the entanglement reaches the maximum value in a short time, with the increase of the mean photon number, the period of entanglement evolution becomes clearly. The degrees of enganglement in a short time become lower due to the atom is initially in the superposition state of all three levels. Compared with the results of using the method of rotating wave approximation, the contribution of the without rotating wave approximation terms increase notably and the quantum entanglement curvies displays small zigzag-shaped oscillation, with the increasing of couplings and mean photon number.
The quantum entanglement of the two mode coherent field interacting with a cascade three-level atom was calculated accurately with non-rotating wave approximation by using the complete quantum theory.The influences of the superposition between different atomic energy level at the initial time and the mean photon number on quantum entanglement evolution were considered.The results obtained by the numerical method show that the period of the quantum entanglement evolution becomes longer with the increase of the mean photon number when the atom initially at the single energy level,the quantum entanglement at the first few periods is reduced notably due to the fact of the atom is initially in the superposition state,it takes longer time for the entanglement to reach the maximum value with the increase of the mean photon number,moreover,because of the atom is initially in the superposition state,the periodic disappears.No matter which atom state,the quick oscillation due to the virtual photon process increases with the increasing of the mean photon number.
The entanglement between two Λ-type three-level atoms interacting with coherent field in a dissipative cavity is investigated by means of the entanglement degree of quantum conditional entropy.A solution of the master equation is obtained by super operator method.The authors discuss the entanglement between the two atoms based on two kinds of different initial states(|ψa(0),|Φa(0)) and analyze the influence of decay coefficient of the cavity and mean photon number of the field on entanglement degree.In conclusion,when the atoms are initially in entangled state |ψa(0),the evolution of the entanglement degree depends on decay coefficient of the cavity and intensity of the field.If there is absence of dissipation,the entanglement degree evolves periodically;otherwise,the entanglement degree decays sharply and approaches a stable value.The weaker the intensity of the field is,the greater the stable value becomes.The greater the decay coefficient is,the faster it reaches the stable value.But for the other initial entangled state |Φa(0),the entanglement between the two atoms doesn't evolve with the time.It implies that the entangled state |Φa(0) can be preserved in such a dissipative system.
Using the negative entropy method,the quantum entanglement character of the system of the coherent optical field interacting with the moving atom is studied.The influences of the atomic initial state,the field-mode structure parameter,the average photon number of the coherent field,the detuning,and the transition photon number on the entanglement character of the system are discussed.The result shows that the value of the entanglement degree of the system appears regular evolution and entanglement sudden death phenomenon(ESD)when the atomic motion is considered.When the atomic initial state tends to pure state,the entanglement degree of the system is larger relatively.With the increase of the average photon number of the coherent field,the value of the entanglement degree of the system becomes small,but the period for the regular evolution is almost unchanged.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.
Quantum entanglement between a squeezed coherent state and a Λ-type three level atom was studied via quantum entropy theory.The results show that the maximal degree of entanglement depends on the initial state parameters of the atom,squeezing factor,coherent amplitude factor,and the ratio of detuning to coupling constant.The entanglement strengthens with the increasing of squeezing factor of light.The entanglement occurs periodic evolution with the increasing of the ratio of detuning to coupling constant,the system appears disentanglement.When the ratio of detuning to coupling constant becomes larger,the entanglement between the field and atoms shows periodical change.The system appears steady and maximal entanglement state periodically as the ratio of detuning to coupling constant is sufficiently large.
In this article,the time evolution properties of the field entropy in the system of the two identical two-level entangled atoms interacting with the single-mode coherent light field are studied by means of full quantum theory.The influences of the initial states and the degree of entanglement of two identical two-level entangled atoms and the intensity of the light field on the field entropy are discussed by numerical calculations.The results show that the average value and the oscillation frequency of the field entropy increases with the increasing of the mean photon number,the oscillation of the field entropy presents stated periods in the weak light field and presents collapses and revivals in the increased light field,the amplitudes of field entropy increase with increasing initial degree of entanglement of two entangled atoms.
In this paper, the quantum entanglement between a single mode binomial field and a cascade three-level atom is calculated mechanically without the rotating wave approximation. The numerical results indicate that the quantum entanglement at the first few periods is reduced notably due to the fact that the atom is initially in the superposition state. With increasing field parameter , the period of the entanglement evolution becomes obvious and the quantum decoherence phenomenon emerges in a short time.