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Analog of the spin-orbit induced anomalous Hall effect with quantized radiation

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.