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

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