Laser frequency stability has improved rapidly over the past 30 years by elaborately designed reference cavities. To date, the best laser frequency stability is 4×10^-17 for averaging times from 0.8 s to a few tens of seconds. This is done by stabilizing a laser to a single crystal silicon Fabry-Pérot resonator at 124 K. The fundamental limit of this type of cavities is the thermal Brownian noise of the mirror coatings and the spacer.

In addition to using the excellent intrinsic mechanical and thermal properties of the material, locking to a narrow atomic transition is another way to stabilize the laser frequency. Narrow spectral holes in rare earth ion crystals not only give a narrow transition spectrum, but also a slow light effect. Laser frequency stabilization using hole-burning has been demonstrated  to reach a stability comparable to reference cavities. We are going to use the slow light effect induced by spectral hole burning to stabilize the laser frequency. The strong dispersion inside the spectral hole will significantly slow down the group velocity of the light traveling in the crystal cavity to a small fraction of its speed in vacuum. A reduction of group velocity by four orders of magnitude has been demonstrated in our group. This is equivalent to increase the cavity length by a corresponding factor. Two other important parameters for a cavity-type reference are the vibration sensitivity and the thermal Brownian noise, which are reduced by the slow light effect and the cryogenic temperature, respectively. This project aims to study the fundamental limit of this type of laser stabilization and to demonstrate it experimentally.

Fig. Y₂SiO₅ crystal cavity (6 mm long) transmission spectrum (red trace), absorption spectrum (black trace) and refractive index spectrum (blue trace) around an 18 MHz spectral hole. The slow light effect is caused by the strong dispersion inside the spectral hole, the extracted group velocity is 3 orders of magnitude smaller than without the spectral hole.