  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 mesoscopicaly 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.
