  We study the dynamics of two two-level atoms embedded near to the interface
of paired meta-material slabs, one of negative permeability and the other of
negative permittivity. The interface behaves as a plasmonic waveguide composed
of surface-plasmon polariton modes. It is found that significantly different
dynamics occur for the resonant and an off-resonant couplings of the plasma
field to the atoms. In the case of the resonant coupling, the plasma field does
not appear as a dissipative reservoir to the atoms. We adopt the image method
and show that the dynamics of the two atoms are completely equivalent to those
of a four-atom system. Moreover, two threshold coupling strengths exist, one
corresponding to the strength of coupling of the plasma field to the symmetric
and the other the antisymmetric mode of the two-atom system. The thresholds
distinguish between the non-Markovian (memory preserving) and Markovian
(memoryless) regimes of the evolutions that different time scales of the
evolution of the memory effects and entanglement can be observed. The Markovian
regime is characterized by exponentially decaying whereas the non-Markovian
regime by sinusoidally oscillating contributions to the evolution of the
probability amplitudes. The solutions predict a large and long living
entanglement mediated by the plasma field in both Markovian and non-Markovian
regimes of the evolution. We also show that a simultaneous Markovian and
non-Markovian regime of the evolution may occur in which the memory effects
exist over a finite evolution time. In the case of an off-resonant coupling of
the atoms to the plasma field, the atoms interact with each other by exchanging
virtual photons which results in the dynamics corresponding to those of two
atoms coupled to a common reservoir. In addition, the entanglement is
significantly enhanced under the off-resonant coupling.
