  We present a light-matter interface which consists of a single $^{174}$Yb$^+$
ion coupled to an optical fiber-cavity. We observe that photons at 935 nm are
mainly emitted into the cavity mode and that correlations between the
polarization of the photon and the spin state of the ion are preserved despite
the intrinsic coupling into a single-mode fiber. Complementary, when a faint
coherent light field is injected into the cavity mode we find enhanced and
polarization dependent absorption by the ion.
