  We consider the self-localization of neutral impurity atoms in a
Bose-Einstein condensate in a 1D model. Within the strong coupling approach, we
show that the self-localized state exhibits parametric soliton behavior. The
corresponding stationary states are analogous to the solitons of non-linear
optics and to the solitonic solutions of the Schroedinger-Newton equation
(which appears in models that consider the connection between quantum mechanics
and gravitation). In addition, we present a Bogoliubov-de-Gennes formalism to
describe the quantum fluctuations around the product state of the strong
coupling description. Our fluctuation calculations yield the excitation
spectrum and reveal considerable corrections to the strong coupling
description. The knowledge of the spectrum allows a spectroscopic detection of
the impurity self-localization phenomenon.
