  We investigate the rotation of the polarization of a light ray propagating in
the gravitational field of a circularly polarized laser beam. The rotation
consists of a reciprocal part due to gravitational optical activity, and a
non-reciprocal part due to the gravitational Faraday effect. We discuss how to
distinguish the two effects: Letting light propagate back and forth between two
mirrors, the rotation due to gravitational optical activity cancels while the
rotation due to the gravitational Faraday effect accumulates. In contrast, the
rotation due to both effects accumulates in a ring cavity and a situation can
be created in which gravitational optical activity dominates. Such setups
amplify the effects by up to five orders of magnitude, which however is not
enough to make them measurable with state of the art technology. The effects
are of conceptual interest as they reveal gravitational spin-spin coupling in
the realm of classical general relativity, a phenomenon which occurs in
perturbative quantum gravity.
