Laser stabilization using spectral hole burning

We have frequency stabilized a Coherent CR699-21 dye laser to a transient spectral hole on the 606 nm transition in Pr^{+3}:Y_2SiO_5. A frequency stability of 1 kHz has been obtained on the 10 microsecond timescale together with a long-term frequency drift below 1 kHz/s. RF magnetic fields are used to repopulate the hyperfine levels allowing us to control the dynamics of the spectral hole. A detailed theory of the atomic response to laser frequency errors has been developed which allows us to design and optimize the laser stabilization feedback loop, and specifically we give a stability criterion that must be fulfilled in order to obtain very low drift rates. The laser stability is sufficient for performing quantum gate experiments in Pr^{+3}:Y_2SiO_5.