Using slow light to enable laser frequency stabilization to a short, high-Q cavity
State-of-the-art laser frequency stabilization is limited by miniscule length changes caused by thermal noise. In this work, a cavity-length-insensitive frequency stabilization scheme is implemented using strong dispersion in a $21\,\mathrm{mm}$ long cavity with a europium-ion-doped spacer of yttrium orthosilicate. A number of limiting factors for slow light laser stabilization are evaluated, including the inhomogeneous and homogeneous linewidth of the ions, the deterioration of spectral windows, and the linewidth of the cavity modes. Using strong dispersion, the cavity modes were narrowed by a factor $1.6\cdot 10^5$, leading to a cavity linewidth of $3.0\,\mathrm{kHz}$ and a $Q$ factor of $1.7\cdot 10^{11}$. Frequency stabilization was demonstrated using a cavity mode in a spectral transparency region near the center of the inhomogeneous profile, showing an overlapping Allan deviation below $6\cdot 10^{-14}$ and a linear drift rate of $3.66\,\mathrm{Hz}/\mathrm{s}$. Considering improvements that could be implemented, this makes the europium-based slow light laser frequency reference a promising candidate for ultra-precise tabletop frequency stabilization.