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Chinese Physics

Entanglement between two atoms in the system of Schrödinger cat state interacting with two entangled atoms

Tang-Kun Liu

Published Nov 1, 2007• 3 citations
Publisher

Abstract

By the negative eigenvalues of partial transposition of density matrix, this paper investigates the time evolution of entanglement of the two entangled atoms in the system of two atoms interacting with Schrödinger cat state. The result shows that the two atoms are always in the entanglement state, and the degree of entanglement between the two atoms exhibits ordinary collapses and revivals at 0.2 degree of entanglement, when the light field is large enough. On the other hand, the reinforcement of three different light fields on the degree of entanglement between two atoms is not evident.

DOI
10.1088/1009-1963/16/11/042

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By the negative eigenvalues of partial transposition of density matrix, this paper investigates the time evolution of entanglement of the two entangled atoms in the system of two atoms interacting with Schrödinger cat state. The result shows that the two atoms are always in the entanglement state, and the degree of entanglement between the two atoms exhibits ordinary collapses and revivals at 0.2 degree of entanglement, when the light field is large enough. On the other hand, the reinforcement of three different light fields on the degree of entanglement between two atoms is not evident.
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 field entropy can be regarded as a measurement of the degree of entanglement between the light field and the atoms of a system which is composed of two-level atoms initially in an entangled state interacting with the Schrödinger cat state. The influences of the strength of light field and the phase angle between the two coherent states on the field entropy are discussed by using numerical calculations. The result shows that when the strength of light field is large enough the field entropy is not zero and the degrees of entanglement between the atoms and the three different states of the light fields are equal. When the strength of the light field is small, the degree of entanglement is maximum in a system of the two entangled atoms interacting with an odd coherent state; it is intermediate for a system of the two entangled atoms interacting with the Yurke–Stoler coherent state and it is minimum in a system of the two entangled atoms interacting with an even coherent state.
The field entropy evolution of a system which is composed of two moving entangled atoms interacting with the Schrdinger cat state is studied by means of the full quantum theory.The influences of the strength of light field,the phase angle between the two coherent states,the atomic motion and the field-model structure parameter on the field entropy are discussed.The result shows that the atomic motion leads to the periodic evolution of the field entropy.When the strength of light field is small,the degree of entanglement is maximum in a system of the moving atoms interacting with an odd coherent state;it is intermediate for a system of the the moving atoms interacting with Yurke-Stoler coherent state,and it is minimum in a system of the moving atoms interacting with an even coherent state.When the strength of light field is large enough,the degrees of entanglement between the moving atoms and the three different states of the light fields become equal,and the properties of field entropy evolvement are also same.With increasing atomic speed or field-model structure parameter,the evolution period of the field entropy is shortter,the degree of entanglement between field and moving atoms is weaker.
Based on the quantum information theory, this paper has investigated the entanglement properties of a system which is composed of the two entangled two-level atoms interacting with the two-mode entangled coherent fields. The influences of the strength of light field and the two parameters of entanglement between the two-mode fields on the field entropy and on the negative eigenvalues of partial transposition of density matrix are discussed by using numerical calculations. The result shows that the entanglement properties in a system of a pairwise entangled states can be controlled by appropriately choosing the two parameters of entanglement between the two-mode entangled coherent fields and the strength of two light fields respectively.
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.