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Acta Physica Sinica

Entanglement of a Λ-type three-level atom with a single-mode field initially in the number state

Qingchun Zhou, Zhu Shi-Ning, (1)南京大学物理系，固体微结构国家重点实验室，南京 210093; (2)南京大学物理系，固体微结构国家重点实验室，南京 210093;华东船舶工业学院数理系，镇江 212003

Published Jan 1, 2005• 5 citations
Publisher

Abstract

The time evolution of entanglement and disentanglement between a Λ-type three-l evel atom and a single-mode field initially in the number state in an ideal cavi ty are investigated by considering von Neumann entropy of the optical field. Res ults indicate that entanglement of the system displays periodicity; the maximal degree of entanglement depends on the initial atomic state, the initial photon n umber and the ratio of detuning to the coupling constant, while the number of ti mes for maximal entanglement and disentanglement in a period is independent of t he initial photon number. The initial relative phase between the two lower state s have effects on the time evolution of field entropy, while the initial relativ e phases between the excited state and the ground states of the atom does not.

DOI
10.7498/aps.54.2043

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The time evolution of entanglement and disentanglement between a Λ-type three-l evel atom and a single-mode field initially in the number state in an ideal cavi ty are investigated by considering von Neumann entropy of the optical field. Res ults indicate that entanglement of the system displays periodicity; the maximal degree of entanglement depends on the initial atomic state, the initial photon n umber and the ratio of detuning to the coupling constant, while the number of ti mes for maximal entanglement and disentanglement in a period is independent of t he initial photon number. The initial relative phase between the two lower state s have effects on the time evolution of field entropy, while the initial relativ e phases between the excited state and the ground states of the atom does not.
We investigate the evolution of the atomic quantum entropy and the atom–field entanglement in a system of a Λ-configuration three-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system, we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium, and the intensity-dependent coupling functional on the entropy are analyzed.
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.
We investigate the evolution of the atomic quantum entropy and the atom–field entanglement in a system of a Λ-configuration three-level atom interacting with a two-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a non-correlated two-mode squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are analysed.
We investigate the Raman coupled model of two entangled Λ-type three-level atoms interacting with a two-mode quantized cavity field.With the negative eignevalues of the partial transposition matrix,we obtain the time evolution of entanglement between the two atoms.The results show that the entanglement of the two atoms displays periodicity;the evolution regular of entanglement is influenced by the initial state of two atoms and initial photon number of the cavity.For special initial state,the two-atom quantum state will stay in the maximum entangled state forever and have no relation with the initial photon number.Compared with Tavis-Commings model,the entanglement of the two atoms can live for much longer time in the proposed model.
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.
We investigate the evolution of the atomic quantum entropy and the atom-field entanglement in a system of a Ξ-configuration three-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system, we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are analyzed.