  We demonstrate how the term describing interaction between a single two-level
atom and two cavity field modes may attain a Rashba form. As an outcome, cavity
QED provides a testbed for studies of phenomena reminiscent of the spin-orbit
induced anomalous Hall effect. The effective magnetic field, deriving from the
non-Abelian gauge potentials rendered by the Rashba coupling, induces a
transverse force acting on the phase space distributions. Thereby, the phase
space distributions build up a transverse motion manifesting itself in spiral
trajectories, rather than circular ones obtained for a zero magnetic field as
one would acquire for the corresponding Abelian gauge potentials. Utilizing
realistic experimental parameters, the phenomenon is numerically verified,
ascertain that it should be realizable with current techniques.
