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Acta Physica Sinica

Entanglement and intrinsic decoherence in the interaction between two-mode field and atom

Xia Tan, Zhang Cheng-qiang, Yun‐Jie Xia, 曲阜师范大学物理工程学院,曲阜 273165

Published Jan 1, 2006• 5 citations
Publisher

Abstract

Considering the interaction between two-mode SU(1,1) coherence states and a two-level atom, we find an exact solution of the Milburn equation for the system. We investigate the time evolution of the entanglement of field-atom and one of two modes of field using the quantum-reduced entropy and quantum relative entropy, respectively. The influences of intrinsic decoherence and two-mode photon number difference on the evolution of the entanglement of field-atom and one of two modes of field are discussed. It is shown that the entanglement of field-atom reduces to a stationary value with time evolution and the entanglement between two modes increases to another stationary value with intrinsic decoherence, and the values only depend on the two-mode photon number and mean photon number.

DOI
10.7498/aps.55.2263

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Considering the interaction between two-mode SU(1,1) coherence states and a two-level atom, we find an exact solution of the Milburn equation for the system. We investigate the time evolution of the entanglement of field-atom and one of two modes of field using the quantum-reduced entropy and quantum relative entropy, respectively. The influences of intrinsic decoherence and two-mode photon number difference on the evolution of the entanglement of field-atom and one of two modes of field are discussed. It is shown that the entanglement of field-atom reduces to a stationary value with time evolution and the entanglement between two modes increases to another stationary value with intrinsic decoherence, and the values only depend on the two-mode photon number and mean photon number.
How the mean photon number,the probability of excited state and intrinsic decoherence coefficient influence the time evolution of entanglement is unknown,when a single-mode quantized optic field and a two-level atom coupling system is governed by Milburn equation.The Jaynes-Cummings model is considered.A lower bound of concurrence is proposed to calculate the entanglement.Simulation results indicate that the entanglement of system increases following the increasing of intrinsic decoherence coefficient or the decreasing of the mean photon number.Besides that,the entanglement of the system decreases,while the probability of the exited state increases from 0 to 0.1,and increases,while the probability of the exited state increases from 0.1 to 1.
The field entropy evolution in a system of the Schrodinger cat state light field interacting with a two-level atom was studied by solving Milburn equation.The influence of intrinsic decoherence,the strength of light field and the phase angle between the two coherence states on the field entropy evolution was discussed.The results show that the field entropy vibration will be weak gradually because of the intrinsic decoherence,and the degree of entanglement in the field-atom system approaches to a certain value with time evolution.Furthermore,the degree of entanglement in the field-atom system only depends on the strength of light field and the phase angle between the two coherence states,and have nothing to do with intrinsic decoherence.When the strength of light field is relatively small,the degree of entanglement is maximum in a system of a two-level atom interacting with an odd coherence state light field,and it is minimum in a system of a two-level atom interacting with an even coherence state light field;it is intermediate for a system of a two-level atom interacting with Yurke-Stoler coherence state light field.When the intrinsic decoherence is fixed and the strength of light field is relatively large,the degree of entanglement in the field-atom system existing in the Yurke-stoler,the even coherence state and odd coherence state tends to the same.
We investigate the system of Bose-Einstein condensates interacting with SU(1, 1) coherent state in two-photon transition process, the entanglement of atom-field and the entanglement between the two-mode light field using the quantum reduced entropy and quantum relative entropy are studied, respectively . The influences of the coherent parameter of light field, two-mode photon number difference and interaction between atoms on the evolution of the entanglement of atom-field and the entanglement between the two-mode light field have been discussed.
The quantum statistical properties in the system of a two-mode SU(1,1)coherent field interacting with a two-level atom are investigated by solving Milburn equation.The effects on the quantum statistical properties induced by the intrinsic decoherence,the two-mode photon number and the mean photon number are analyzed.The results show that the intrinsic decoherence strengthens the anti-bunching effect of the two-mode and the correlation intensity between the two modes and makes the first mode of the field always to be sub-Poissonian.The second-order coherence degree of the two-mode field also exhibits obvious collapse- revival effect with the intrinsic decoherence.The first mode of the field is sub-Poissonian with the evolution of the time.The photon anti-bunching appears and the correlation between the two modes of light is both positive and non-classical.But in most of the time,the second mode of the field is Poissonian with the evolution of the time and the photon bunching appears.
In the consideration of Milburn model of intrinsic decoherence,we investigate the entanglement between two two-level atoms interacting with a Fock state of single-mode quantized radiation field.The reduced density matrix of the atom system is given explicitly.Due to the intrinsic decoherence,the entanglement of the atoms will decrease as the evolution of the system.And finally,the atoms system will approach a stationary state which the stationary entanglement depends on the initial states of the field and the atoms.Here,the entanglement is calculated by making use of the concurrence.
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.