Collective dynamics of atoms embedded into negative index materials

The dynamics of two two-level atoms embedded near to the interface of paired metamaterial slabs, one of negative permeability and the other of negative permittivity are studied. 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 to the antisymmetric modes of the system. The thresholds distinguish between the non-Markovian and Markovian regimes of the evolutions. 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 regimes of the evolution may occur in which the memory effects exist over a finite evolution time. Keywords: met