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We study the dynamics of two two-level atoms embedded near to the interfaceof paired meta-material slabs, one of negative permeability and the other ofnegative permittivity. The interface behaves as a plasmonic waveguide composedof surface-plasmon polariton modes. It is found that significantly differentdynamics occur for the resonant and an off-resonant couplings of the plasmafield to the atoms. In the case of the resonant coupling, the plasma field doesnot appear as a dissipative reservoir to the atoms. We adopt the image methodand show that the dynamics of the two atoms are completely equivalent to thoseof a four-atom system. Moreover, two threshold coupling strengths exist, onecorresponding to the strength of coupling of the plasma field to the symmetricand the other the antisymmetric mode of the two-atom system. The thresholdsdistinguish between the non-Markovian (memory preserving) and Markovian(memoryless) regimes of the evolutions that different time scales of theevolution of the memory effects and entanglement can be observed. The Markovianregime is characterized by exponentially decaying whereas the non-Markovianregime by sinusoidally oscillating contributions to the evolution of theprobability amplitudes. The solutions predict a large and long livingentanglement mediated by the plasma field in both Markovian and non-Markovianregimes of the evolution. We also show that a simultaneous Markovian andnon-Markovian regime of the evolution may occur in which the memory effectsexist over a finite evolution time. In the case of an off-resonant coupling ofthe atoms to the plasma field, the atoms interact with each other by exchangingvirtual photons which results in the dynamics corresponding to those of twoatoms coupled to a common reservoir. In addition, the entanglement issignificantly enhanced under the off-resonant coupling.

Collective dynamics and entanglement of two atoms embedded into negative index material