  Green functions scattering method is generalized to consider mixing of
electromagnetic polarizations after reflection from the plane boundary between
different media and applied to derivation of the Casimir-Polder potential in
systems with Chern-Simons plane boundary layers. The method is first applied to
derive the Casimir-Polder potential of an anisotropic atom in the presence of a
Chern-Simons plane boundary layer on a dielectric half-space. Then a general
result for the Casimir-Polder potential of an anisotropic atom between two
dielectric half-spaces with Chern-Simons plane parallel boundary layers is
derived. The Casimir-Polder potential of an anisotropic atom between two
Chern-Simons plane parallel layers in vacuum is expressed through special
functions. Novel P-odd three-body vacuum effects are discovered and analyzed in
the system of two Chern-Simons plane parallel layers and a neutral atom in its
ground state between the layers. Remarkably, P-odd three-body vacuum effects
arising due to 180 degree rotation of one of the Chern-Simons layers can be
verified in experiments with neutral atoms having QED dipole interaction with
an electromagnetic field.
