  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.
