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Chinese Physics

Entropy evolvement properties in a system of Schrödinger cat state light field interacting with two entangled atoms

Tang-Kun Liu

Published Mar 1, 2006• 11 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/15/3/016

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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.
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.
In this paper, we use the field entropy as a measurement of the degree of entanglement between the light field and the atoms of the system which is composed of two dipole–dipole interacting two-level atoms initially in an entangled state interacting with the single mode coherent field in a Kerr medium. The influence of the coupling constant of dipole–dipole interaction between atoms and the coupling strength of the Kerr medium with the light field and the intensity of the light field on the field entropy are discussed by numerical calculations. It is shown that when the coupling strength of the Kerr medium with the light field is large enough and the light field is strong, the degree of entanglement between the atoms with the light field becomes weaker. The degree of entanglement only changes slightly with the change of the coupling constant of dipole–dipole interaction between atoms.
In this article,the time evolution properties of the field entropy in the system of the two identical two-level entangled atoms interacting with the single-mode coherent light field are studied by means of full quantum theory.The influences of the initial states and the degree of entanglement of two identical two-level entangled atoms and the intensity of the light field on the field entropy are discussed by numerical calculations.The results show that the average value and the oscillation frequency of the field entropy increases with the increasing of the mean photon number,the oscillation of the field entropy presents stated periods in the weak light field and presents collapses and revivals in the increased light field,the amplitudes of field entropy increase with increasing initial degree of entanglement of two entangled atoms.
According to the complete quantum theory,the quantum field-entropy evolution properties in a system of the two coupled two-level atoms interacting with a single-mode odd-coherent state light field are studied.Through numerical calculation the influence of the initial mean photon number n_0,the coupled intensity g of interaction between the single-mode field and atoms,and the coupled intensity g_a of dipole-dipole interaction between the two coupled atoms on the quantum field-entropy evolving while the initial state of the light field is a single-mode odd-coherent and the two coupled two-level atoms lay in different Einstein Poclolsky Rosen(EPR) entangled state respectively.The results indicate that the time evolving of quantum field-entropy is closely related to the initial atoms state.The quantum field-entropy evolution can display the phenomena of entanglement and disentanglement while they are periodically under the condition of intensity field(n_01). Meanwhile the phenomena of quantum interference is also discovered.The periodicity of the quantum field-entropy anomalous oscillation decreases gradually with the increasing of g values.When g_a is an especial constant,it is shown that the phenomena of period collapse-reversion can present.
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.