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Journal of Optoelectronics·laser

Tripartite entanglement properties among atoms in three Jaynes-Cummings model

LU Dao-ming

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

In this paper we consider the situation that three identical two-level atoms resonantly interact with three distant single-mode optical cavities via a one-photon hopping separately.Three atoms are in like-GHz state and therr optical cavities are all in vacuum state initially.Using the Jaynes-Cummings,the time evolution of the system is given.We adopt the entanglement tensor approach to quantify the degree of entanglement.The tripartite entanglement dynamics among three atoms and the entanglement dynamics between two atoms are studied.The influence of atomic states initially on tripartite entanglement among atoms and two-body entanglement between two atoms are discussed.The results obtained using the numerical method show:first,the time evolution of tripartite entanglement displays the periodic oscillation behavior and its oscillation period is not realted with the initial degree of entanglement among atmos;second the peak and mean of entanglement measures E3 and F2 incease with increasing of the initial degree of entanglement among atmos,which means that the larger the initial degree of entanglement among atoms,the layer the tripartite entanglement among atoms and the two-body entanglement between atoms;third,the phenomenon of sudden death of entanglement between two atoms occurs,and the length of the death time interval decreases with increasing of the initial degree of entanglement among atoms.This shows that the length of the death time interval of two-body entanglement can be decreased by selecting initially atomic state with high degree of entanglement among atoms.

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In this paper we consider the situation that three identical two-level atoms resonantly interact with three distant single-mode optical cavities via a one-photon hopping separately.Three atoms are in like-GHz state and therr optical cavities are all in vacuum state initially.Using the Jaynes-Cummings,the time evolution of the system is given.We adopt the entanglement tensor approach to quantify the degree of entanglement.The tripartite entanglement dynamics among three atoms and the entanglement dynamics between two atoms are studied.The influence of atomic states initially on tripartite entanglement among atoms and two-body entanglement between two atoms are discussed.The results obtained using the numerical method show:first,the time evolution of tripartite entanglement displays the periodic oscillation behavior and its oscillation period is not realted with the initial degree of entanglement among atmos;second the peak and mean of entanglement measures E3 and F2 incease with increasing of the initial degree of entanglement among atmos,which means that the larger the initial degree of entanglement among atoms,the layer the tripartite entanglement among atoms and the two-body entanglement between atoms;third,the phenomenon of sudden death of entanglement between two atoms occurs,and the length of the death time interval decreases with increasing of the initial degree of entanglement among atoms.This shows that the length of the death time interval of two-body entanglement can be decreased by selecting initially atomic state with high degree of entanglement among atoms.
In this paper we consider the situation that four identical two-level atoms are separately trapped in coupled single-mode optical cavities and each atom resonantly interacts with cavity via a one-photon hopping. The three-body entanglement dynamics in each cavity is studied. The influences of atom-cavity coupling constant on the three-body entanglement are discussed. The results obtained using the numerical method show that the three-body entanglement displays the collapse-revival phenomena when atom-cavity coupling constant is larger than a fixed value. On the other hand, the three-body entanglement is the result of the coherent superposition of the two-body entanglements.
We study the Bell-nonlocality dynamics of three remote atoms, two of which are trapped in one single-mode cavity and the third atom is trapped in another remote single-mode cavity. The interactions between the atoms and the cavity modes are studied via Tavis Cummings and Jaynes Cummings models. Here, the two single-mode cavities are introduced to simulate two different enviroments of the three atoms. The tripartite nonlocal correlations are studied in terms of the Svetlichny inequality and the WWZB inequality, respectively. The results show that the tripartite Bell-nonlocality sudden death will occur for the W state and GHZ state initial conditions. The detailed results demonstrate that the tripartite nonlocality of GHZ state is more robust than that of W state when suffering from the effect of environments.
Extending the double Jaynes–Cummings model to a more complicated case where the mode–mode competition is considered, we investigate the entanglement character of two isolated atoms by means of concurrence, and discuss the dependence of atom–atom entanglement on the different initial state and the relative coupling strength between the atom and the corresponding cavity field. The results show that the amplitude and the period of the atom–atom entanglement evolution can be controlled by the choice of initial state and relative coupling strength, respectively. We find that the phenomenon of entanglement sudden death (ESD) is sensitive to the initial conditions. The length of the time interval for zero entanglement depends not only on the initial degree of entanglement between two atoms but also on the relative coupling strength of atom–field interaction. The ESD effect can be weakened by enhancing the mode–mode competition between the three- and single-photon processes.
Quantum entanglement is one of most remarkable features of quantum mechanics,and in recent years it has played a more and more important role in quantum information.However,real quantum system inevitably interacts with the environment,resulting in the entanglement decay or even entanglement sudden death,so it is necessary to study the entanglement dynamical properties of an open system under different environments.In this paper,we investigate the entanglement dynamic behaviors of three interacting two-level atoms in an optical cavity which is coupled to a structured zero-temperature bosonic reservoir.Laplace transform,LBC and other methods are utilized,through numerical method we analyze the entanglement dynamic behavios of tripartite of three atoms and bipartite of cavity and reservoir.We also discuss how the coupling parameters affect the entanglement dynamics.Results show that in a short time,the entanglement of tripartite increases with coupling strength of three atoms increasing,and a periodic oscillation appears, but entanglement of bipartite decreases.The entanglement of tripartite decreases with the coupling strength between atoms and cavity increasing and damping oscillation appears,but the entanglement of bipartite increases.In a long-time limit,the entanglement approaches to a steady value.The non-Markovian dynamics of the qubits is determined by both the coupling strength and the spectral width.The strong system-reservoir coupling regime results in the non-Markovian dynamics of system.As the spectral width increases,the system of three atoms transforms from non-Markovian regime to Markovian regime.The increasing of spectral width results in the Markovian dynamic behavior of system,but the system of the atoms falls into the non-Markovian regime once more.When the coupling between the cavity and reservoir is weak,the entanglement of three atoms increases as the detuning of the cavity and reservoir increases,but it is not obvious.When the coupling between the cavity and reservoir is strong,the entanglement of three atoms increases and a periodic oscillation appears with increasing the detuning between the cavity and reservoir,so we can effectively restrain the effects of dissipation of reservoir on entanglement decay by adjusting the detuning between the cavity and reservoir.
Based on the exactly analytic solution obtained of the intensity-dependent Jaynes–Cummings model for a certain class of initial entangled mixed states, we explore the time evolution of the entanglement between two atoms, initially non-locally correlated and separately interacting with two distinct cavities. The results show that entanglement sudden death is dependent on the different initial states of atoms, and the length of the time interval for the zero entanglement is invariant for a certain class of initial mixed states.
In this paper we consider the case that three identical two-level atoms are trapped in a single-mode cavity which is in a weak coherent state initially, and there is an interaction between two atoms. The tripartite entanglement dynamics among atoms is studied. The influences of atom-atom coupling constant and intensity of the cavity field on the tripartite entanglement among atoms are discussed. The results obtained using the numerical method show that the tripartite entanglement among atoms is strengthened with the increase of intensity of the cavity field; on the other hand, it is weakened with the increase of the coupling constant between atoms.