The Non-markovian Behavior Of A V-type Three-level Atom In Double Layer Single-negative Meta-materials

In the studying of open quantum system, we always have different treatments for the interaction between the environment and quantum systems, generally the most common method we used is the Markovian approximation, which ignored the influ-ence of the environment on the system. This paper we studied the non-Markovian dynamic between the atomic and plasma mode with Lorentzian form under the differ-ent coupling strength. In this article, we through the introduction of electromagnetic wave propagation in the medium, deriving the Green function of the multilayered medium system, thus get the dipole field of the multilayered medium system. Using it and the characteristics of single-negative metamaterials, we get the surface plasmon mode with the Lorentzian form, which has the similar features with the high-quality single-mode cavity. And then we studied the influence to the bandwidth of Lorentzian with the change of the dissipaton of the metamaterials. Then we analyzed the in-teraction between the V-type three-level atom and the surface plasma mode, and discussed the change of non-Markovian behavior with the different Lorentzian model and the different relative angle between the two transition dipole moment’s.