Enhanced stability from co-resonant cavities in a monolithic array

We demonstrate a micro-Fabry-P\'erot cavity array through laser etching of high-surface-quality mirrors onto a single fused silica substrate. A cavity finesse of $4750\pm 200$ was achieved with a simple array design with $500~\mu m$ cavity length, $100~\mu m$ diameter micromirrors and $300~\mu m$ transverse separation. Arrays with up to 12 cavities were simultaneously tested for single mode operation, and absolute frequency measurements correlated strongly with the etched depth as measured by profilometry. Simultaneous measurements of the absolute resonant frequency for neighboring cavities showed a factor of 5 common-mode cavity drift reduction. Arrays of such cavities can be employed in chip-scale cavity QED networks (current cooperativity estimates are at the border of strong coupling for $^{87}$Rb atoms, $C=1$) as well as for precise laser stabilization at nearby wavelengths on a chip.