Photonic versus electronic quantum anomalous Hall effect

We derive the diagram of the topological phases accessible within a generic Hamiltonian describing quantum anomalous Hall effect for photons and electrons in honeycomb lattices in the presence of a Zeeman field and spin- orbit coupling (SOC). The two cases differ crucially by the winding number of their SOC, which is 1 for the Rashba SOC of electrons, and 2 for the photon SOC induced by the energy splitting between the TE and TM modes. As a consequence, the two models exhibit opposite Chern numbers +/- 2 at low field. Moreover, the photonic system shows a topological transition absent in the electronic case. If the photonic states are mixed with excitonic resonances to form interacting exciton- polaritons, the effective Zeeman field can be induced and controlled by a circularly polarized pump. This new feature allows an all-optical control of the topological phase transitions.