Stabilizing an optical cavity containing a bulk diamond crystal at millikelvin temperatures in a cryogen-free dilution refrigerator

We successfully stabilized a Fabry-P\'erot optical cavity incorporating a bulk diamond crystal at millikelvin temperatures in a cryogen-free dilution refrigerator with the pulse-tube cryocooler running. In stark contrast to previous demonstrations where lasers were locked to the cavities, our setup locks the cavity to a laser. Our measurements of cavity length fluctuation suggest that the setup could stabilize a cavity up to a finesse of $1.2\times 10^4$ without the diamond and $5.8 \times10^3$ with the diamond crystal. The finesse with a diamond crystal of approximately 90 is primarily limited by the absorption loss inside the diamond.