Strong coupling cavity QED using rare-earth-ion dopants in monolithic resonators: what you can do with a weak oscillator

We investigate the possibility of achieving the strong coupling regime of cavity quantum electrodynamics using rare earth ions as impurities in monolithic optical resonators. We conclude that due to the weak oscillator strengths of the rare earths, it may be possible but difficult, to reach the regime where the single photon Rabi frequency is large compared to both the cavity and atom decay rates. However reaching the regime where the saturation photon and atom numbers are less than one should be much more achievable. We show that in this `bad cavity' regime, transfer of quantum states and an optical phase shift conditional on the state of the atom is still possible, and suggest a method for coherent detection of single dopants.