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Journal of Modern Physics

Dynamics of Entanglement in the Cavity with Nonlinear Medium

Shao-Jiang Du, Hairan Feng

Published Jan 1, 2013• 1 citation
Publisher

Abstract

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.

DOI
10.4236/jmp.2013.45086

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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.
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.
The entanglement dynamics of system, where atoms A and B interact with single mode cavity fields a and b respectively, is studied. The interaction between atom A and cavity a may be described by using the typical Jaynes–Cummings model, while that between the atom B and cavity b filled with a Kerr medium is of a two-photon process. For a certain initial atom entanglement state, there is an entanglement sudden death effect between the two atoms. The Kerr medium in the cavity b can effectively prevent the undesirable entanglement sudden death from occurring. Also, from the viewpoint of the population dynamics, we discuss why the Kerr medium can do so.
In this paper, the entanglement dynamics of two two-level atoms trapped in coupled cavities with a Kerr medium is investigated. We find that the phenomena of entanglement sudden death (ESD) and entanglement sudden birth (ESB) appear during the evolution process. The influences of initial atomic states, Kerr medium, and cavity—cavity hopping rate on the atom—atom entanglement are discussed. The results obtained by the numerical method show that the atom—atom entanglement is strengthened and even prevented from ESD with increasing cavity—cavity hopping rate and Kerr nonlinearity.
By using the negativity method,we study the entanglement dynamics of two entangled atoms,which are in two levels,that go through the high Q fields in the Fock state one by one.The results shows that the initial state of the two-atom and the field in the Fock state are influenced by the entanglement dynamics of two atoms,and we also make the significant comparison of the two-atom entanglement evolutions in the condition that the two atoms are laid in the QED at the same time.We find that: when the cavity field is in the vacuum state,the two-atom entanglements under these two models evolve periodicity;when we choose the cavity field in a Fock state,the entanglement between the two atoms can appear tobe the phenomenon of entanglement sudden death.Furthermore,we investigate the entanglement transfer problem and the relationship among entanglement sudden death,the initial state,and the number of the Fock state.
The entanglement dynamics of two atoms initially in an entangled state system interacting with a bimodal field is investigated by making use of the concurrence and linear entropy.The effect of the initial entanglement degree of two atoms and the cavity field on the time evolution of concurrence is analyzed.The results show that the phenomenon of sudden death of the entanglement between two atoms occurs.The length of the death time interval is independent of the initial entanglement degree of two atoms.However,the death time depends on the initial entanglement degree of the cavity field.The atom and the field are entangled during all the evolution process.