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ACTA PHOTONICA SINICA

Quantum Entanglement of a Two-Mode Field Interacting with a Cascade Three-level Atom without Rotating Wave Approximation

Cong Hong-l

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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 entanglement time evolution properties of the two atoms in the system of the two identical entangled two-level atoms interacting with coherent field are studied by means of full quantum theory.Using the numerical method,the influence of the initial entanglement of atoms and the intensity of field on the entanglement measuremont-concurrence is discussed.The results show that the peaks of the concurrence oscillations increase with the increasing of the initial degree of entanglement of two entangled atoms.The oscillation of the concurrence presents collapses and revivals with the increasing of the mean photon number,while its periodicity is more and more evident.
The dynamics of a cascade three-level atom interacting with the single mode coherent state under the Counter-Rotating-Wave approximation (C-RWA) is investigated.The properties of the mean-photon number (N(t)) and the degree of second-order coherence (g2(t)) are analyzed in this model.The little indentation which represents the quantum noise of the system appears in the evolution curves of the mean-photon number and the degree of second-order coherence under the C-RWA.The quantum noise which is caused by the virtual photon field gradually becomes weak when ω increases.The quantum noise increases when increases.The anti-bunching effect of the system under the C-RWA is stronger than the one under the RWA.Besides,the relation of N(t) and g2(t) with the atom-field coupling constant λ is revealed in our results.
We investigate the time evolution of the entanglement in the interacting system of a single two-level atom and a single mode coherence field with phase decoherence and discuss the influences of the coupling constant of light and atoms,mean photon number of light and detuning.The results show that the oscillating frequency of the entanglement of the system will increase with the increasing of the coupling constant of light and atoms and the mean photon number of light.The influence of the detuning on time evolution of the entanglement is obvious without phase decoherence and the quantum state of the field and atom will stay in a most entangled state for a long time when the detuning is proper.The phase decoherence causes the fading of entanglement when the system is resonant and it will fade to zero at last.The entanglement of the system is a fading oscillation at first with phase decoherence.The detuning restrains the phase decoherence with the time evolution.In this case the entanglement of the system will not fade to zero at last.The oscillating amplitude of the entanglement is lessening at first and the entanglement will quickly become a constant value with the increasing of detuning.The system will stay in an entangled state with phase decoherence if the detuning is proper.
The entanglement time evolution of atoms in Bell states |β and |β interacting with the two-mode entangled coherent field is investigated by means of full quantum theory and numerical calculations.The effects of the atoms′ initial state,mean photon numbers of field,the degree of the entanglement for the entangled coherent fields,and the coupling strength of interaction between atoms on the entanglement are discussed.The results show that the entropy time evolutions appear regular with the increase of the mean photon numbers of field.The frequency and amplitude of the oscillation decrease with the increase of the coupling strength of interaction between atoms.But when the degree of the entanglement for the entangled coherent fields changes,the frequency and amplitude of the entropy oscillation won′t change.