Excitation spectrum of a multilevel atom coupled with a dielectric nanostructure

We develop a microscopic calculation scheme for the excitation spectrum of a single-electron atom localized near a dielectric nanostructure. The atom originally has an arbitrary degenerate structure of its Zeeman sublevels on its closed optical transition and we follow how the excitation spectrum would be modified by its radiative coupling with a mesoscopically small dielectric sample of arbitrary shape. The dielectric medium is modeled by a dense ensemble of $V$-type atoms having the same dielectric permittivity near the transition frequency of the reference atom. Our numerical simulations predict strong coupling for some specific configurations and then suggest promising options for quantum interface and quantum information processing at the level of single photons and atoms. In particular, the strong resonance interaction between atom(s) and light, propagating through a photonic crystal waveguide, justifies as realistic the scenario of a signal light coupling with a small atomic array consisting of a few atoms. As a potential implication, the directional one-dimensional resonance scattering, expected in such systems, could provide a quantum bus by entangling distant atoms integrated into a quantum register.