Cavity QED based on collective magnetic dipole coupling: spin ensembles as hybrid two-level systems.

We analyze the magnetic dipole coupling of an ensemble of spins to a superconducting microwave stripline structure, incorporating a Josephson junction based transmon qubit. We show that this system is described by an embedded Jaynes-Cummings model: in the strong coupling regime, collective spin-wave excitations of the ensemble of spins pick up the nonlinearity of the cavity mode, such that the two lowest eigenstates of the coupled spin wave-microwave cavity-Josephson junction system define a hybrid two-level system. The proposal described here enables new avenues for nonlinear optics using optical photons coupled to spin ensembles via Raman transitions. The possibility of strong coupling cavity QED with magnetic dipole transitions also opens up the possibility of extending quantum information processing protocols to spins in silicon or graphene, without the need for single-spin confinement.