Strong coupling of a chiral molecule with circularly polarised modes inside a cavity

We consider the discriminatory interaction of a chiral molecule with circularly polarised modes inside a cavity. Starting from a generalised Jaynes--Cummings model that includes both electric and magnetic dipole couplings, we derive the Rabi frequency and associated Casimir--Polder potential for a cavity with a single mode of given handedness. One finds that both acquire a discriminatory component whose sign depends on the relative handedness of molecule and cavity mode. We generalise this result to a cavity that supports two modes of different handedness on the basis of superradiant collective field states.