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The Impact of Kerr Medium on the Evolution Characteristics of Entanglement Degree in the Intensity-dependent Coupling J-C Model

Wang Ju-xia

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The evolution properties of entanglement degree between the light fields and atoms in the additional Kerr medium intensity-dependent coupling J-C model is researched by use of the method of part of the density matrix transpose matrix of negative eigenvalue,and the influence of Kerr medium on entanglement degree can be discussed as well.It is found that the time evolution of atom-field entanglement degree oscillate periodically.The period depends on the strengths of the field-atom coupling and field-medium interaction,and the period becomes smaller with the increase of the strengths.The cycle will reduce gradually with the intensity increasing.The entanglement degree reduces significantly with the number of photons rising or with the strengths of the field-atom coupling and field-medium interaction increasing.The initial state of the field plays an important role in the atom-field entanglement degree.

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The evolution properties of entanglement degree between the light fields and atoms in the additional Kerr medium intensity-dependent coupling J-C model is researched by use of the method of part of the density matrix transpose matrix of negative eigenvalue,and the influence of Kerr medium on entanglement degree can be discussed as well.It is found that the time evolution of atom-field entanglement degree oscillate periodically.The period depends on the strengths of the field-atom coupling and field-medium interaction,and the period becomes smaller with the increase of the strengths.The cycle will reduce gradually with the intensity increasing.The entanglement degree reduces significantly with the number of photons rising or with the strengths of the field-atom coupling and field-medium interaction increasing.The initial state of the field plays an important role in the atom-field entanglement degree.
The atom-field entanglement properties in the intensity-dependent coupling Jaynes-Cummings model with an additional Kerr medium are investigated by using negative eigenvalues ofthe partial transposition matrix of the density matrix.The influences of Kerr medium and initial fieldon atom-field entanglement degree are discussed.The results show that the time evolution of atom-field entanglement degree has the periodicity,for different preparations.The period depends on thestrengthes of the field-atom coupling and field-medium interaction,with the increase of thestrengthes,the period becomes smaller.The initial state of the field plays an important role in the atom-field entanglement degree.
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.
The time evolution of atomic population of the system, where the two identical two-level atoms in Bell states interact with two-mode entangled coherent field in a cavity filled with the Kerr medium, was investigated by means of quantum theory and numerical method. The effects of the atomic initial state, mean photon numbers of field, the degree of the entanglement for the entangled coherent field, and the coupling strength between the Kerr medium and field on the atom’s population are discussed via numerical calculations. The results show that the atomic population is time-independent provided that the atoms are in β11〉 state. For the other three Bell states, there will appear the periodical collapse-revival of atomic population if the initial mean photon number reaches some special values. With the increase of the initial mean photon number, the oscillation frequency of the time-evolution of atomic population increases correspondingly, and the amplitude decreases. The degree of the entanglement of the two-mode entangled coherent field has no effect on the frequency of the Rabi oscillation, but has an obvious effect on the amplitude of Rabi oscillation. When the coupling strength between the Kerr medium and field reaches some special values, it has the obvious effects on the cycle of collapse-revival of atomic population, the frequency and the amplitude of Rabi oscillation.
One of the initial entangled two-atom interact with a high-Q cavity in the single-mode light field.Using the partially transposed matrix of negative eigenvalues(negativity) method we analyse the two-atom entanglement characteristics in a vacuum field,Fock state field and Kerr-media environment,and find that the entanglement of two atoms periodically oscillates in vacuum field,while in the number of particles field entanglement sudden death phenomenon occurs.When the atomic system interacts with the Kerr medium,we obtain that the phenomenon of entanglement sudden death can be eliminated in the particle-number field,and the entanglement of two-atom oscillates aroud a high-value state under certain conditions.
Using the negative entropy method,the quantum entanglement character of the system in J-C model with multi-photon gaussian coupling is studied.The influences of the atomic initial state,the atomic motion,the detuning,the average photon number of the light field and the transition photon number on the entanglement character of the system are discussed.The result shows that the value of the entanglement degree of the system changes in the form of oscillation-stability-oscillation when the atomic motion is considered.The atomic initial state affects the entanglement degree of the system.When the atomic initial state tends to pure state,the entanglement degree of the system is larger relatively.With the increase of the average photon number,the value of the entanglement degree of the system becomes smaller,but the period for the stable value in the time domain is almost unchanged.Increasing the transition photon number,the value of the entanglement degree of the system becomes larger,the period for the stable value in the time domain becomes shorter.As the detuning value increases,the entanglement is disappearing gradually.
In this paper,the field entropy evolution of two coupling atoms interacting with a single mode light field in Kerr medium is studied by means of the quantum theory.It has been shown that:the Kerr medium and the interaction of atoms will influence the periodicity of the evolution of the field entropy,make the connected degree between field and atoms weaken;the excited field intensity also influence the periodicity of the evolution of the field entropy,the connected degree between field and atoms is strengthened first and is weakened later when increases.