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Journal of Atomic and Molecular Physics

The time evolution of atom entanglement in number state field

Qin Dong

Published Jan 1, 2007• 0 citations
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Abstract

Three-atom system is investigated in this paper. Atoms 1 and 2 is entangled initial and is independent with atom 3. The single-mode field is in fock state. We study the time evolution of atoms entanglement when atoms 2 and 3 are in the field. Using partial transposition negative eigenvalue method,we obtain that the entanglement is related strongly with the initial states of the three atomsthe photon numbers of the field and the coupling constants between atoms and cavity.

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Three-atom system is investigated in this paper. Atoms 1 and 2 is entangled initial and is independent with atom 3. The single-mode field is in fock state. We study the time evolution of atoms entanglement when atoms 2 and 3 are in the field. Using partial transposition negative eigenvalue method,we obtain that the entanglement is related strongly with the initial states of the three atomsthe photon numbers of the field and the coupling constants between atoms and cavity.
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.
Based on the entanglement degree of two subsystem which can be measured by the negative eigenvalues of the partial transposition matrix,time evolution of entanglement degree of two atoms in the Tavis-Cummings model,which is interacted with a field in the Fock state,is investigated by numerical methods.When these two atoms are initially prepared in mixed states,the results show that the field in the Fock state,the initial state of two-atom and the coupling constant between the field and the two-atoms have a dramatic influence on the time evolution character of entanglement degree of two atoms.
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.
In the system of two coupling two-level atoms interacting with a single-mode field,effects of atomic initial state and coupling intensity on the entanglement of the quantum system are investigated by the method of negative eigenvalue of the partial transposition matrix.The results demonstrate that the entanglement between the two atoms shows a periodical oscillation,that the entanglement time between the atoms becomes longer and its amplitude becomes larger with increasing atomic initial stateθ,and that the entanglement periodicity between the atoms becomes larger and the subwave diminishes with increasing atomic coupling intensity.
The dynamics of entanglement of three two-level atoms initially in GHZ state system interacting with a Fock state field are investigated by means of concurrence and linear entropy.The effect of photon number on the time evolution of concurrence and linear entropy is analyzed.The results show that the phenomenon of sudden birth of entanglement between two atoms trapped in a cavity occurs and the threshold time and maximum for the creation of the entanglement can be controlled by the photon number.The measurement of the atom outside the cavity leads to the periodic evolution of the concurrence and an increase of the photon number results in decreasing in the maximum of concurrence and shortening of the evolution period of the time behavior of concurrence.