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arXiv:0906.0053 · Communications in Theoretical Physics

Entanglement for a Bimodal Cavity Field Interacting with a Two-Level Atom

Liu Jia, Chen Zi-Yu, Bu Shen-Ping, Zhang Guo-Feng

Published Jul 1, 2009• 3 citations
arXivHTMLPDF

Abstract

Negativity has been adopted to investigate the entanglement in a system composed of a two-level atom and a two-mode cavity field. Effects of Kerr-like medium and the number of photon inside the cavity on the entanglement are studied. Our results show that atomic initial state must be superposed, so that the two cavity field modes can be entangled. Moreover, we also conclude that the number of photon in the two cavity mode should be equal. The interaction between modes, namely, the Kerr effect, has a significant negative contribution. Note that the atom frequency and the cavity frequency have an indistinguishable effect, so a corresponding approximation has been made in this article. These results may be useful for quantum information in optics systems.

DOI
10.1088/0253-6102/52/1/29

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Negativity has been adopted to investigate the entanglement in a system composed of a two-level atom and a two-mode cavity field. Effects of Kerr-like medium and the number of photon inside the cavity on the entanglement are studied. Our results show that atomic initial state must be superposed, so that the two cavity field modes can be entangled. Moreover, we also conclude that the number of photon in the two cavity mode should be equal. The interaction between modes, namely, the Kerr effect, has a significant negative contribution. Note that the atom frequency and the cavity frequency have an indistinguishable effect, so a corresponding approximation has been made in this article. These results may be useful for quantum information in optics systems.
In this article we study the effect of the Kerr-like medium on a system consisting of two-level atom and two fields injected simultaneously within perfect cavity. We assume that in the presence of the nonlinear Kerr coupler, the atom interacts with each field separately. The present system can be regarded as a co-directional nonlinear coupler composed of two Kerr nonlinear waveguides, where the atom–field interaction plays the role of the energy exchange between the waveguides. The system includes two effective different coupling parameters λ 1 and λ 2 , such that each coupling connects the atom with one of the field mode. Moreover, it includes two different susceptibility factors, one represents self-coupling while the other is responsible for cross-action processes. Under certain conditions, the exact solution of the wavefunction in the Schrödinger picture is obtained and the Husimi quasidistribution is derived. A consideration of some physical phenomena, such as collapses and revivals is given, and the degree of entanglement is also discussed. The system is found to be sensitive to the variation of both mean photon numbers as well as to the Kerr-like medium.
Based on the model that one of the two-entangled two-level atoms interacts with the non-degeneration two-photon cavity filled with Kerr medium,the influence of the Kerr effect on the atom and the light is studied such as the average photon numbers,the degrees of second-order coherence and the Cauchy-Schwartz inequality.After selectively detection on one of the atoms at certain particular entanglement degree,it is found that the period of the collapse and revival of the average photon numbers,the degrees of second-order coherence of the lights,and the Cauchy-Schwartz inequality are influenced evidently by the Kerr effect.
The atomic dipole squeezing effect in the system of two identical two-level atoms in the Bell state interacting with the two-mode entangled coherent state field in Kerr medium are investigated by means of solving the Schrdinger equation and numerical calculations. The effects on the atomic dipole squeezing effect produced by the atomic initial state, mean photon number of light field, the degree of the entanglement of the entangled coherent field, the coupling strength of the Kerr medium with the light field and the coupling strength of dipole-dipole interaction between atoms are discussed. The results show that the dipole squeezing effect does not appear for the Bell state |β11>, while there can be dipole squeezing effect under certain conditions for the Bell states |β00> or |β01> or |β10>. In the latter case, the dipole squeezing effect depends on the coupling strength of the Kerr medium with the light field, the mean photon number and the degree of entanglement of the two-mode entangled coherent field.
We investigate the evolution of initial entangled two-atom in cavity with single-mode light field. Using the method of negative eigenvalue of partially transposed matrix we analysis the evolution of the entanglement of the two-atom in a field of number state and Kerr-media environment and find that entanglement sudden death phenomenon occurs in the number of particles field. When the atoms interact with the Kerr medium, we obtain that the phenomenon of sudden death can be eliminated in the particle-number field, and the entanglement of two-atom oscillates around a high-value.
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.