Chip-scale modulation-free laser stabilization using vacuum-gap micro-Fabry-P\'erot cavity

Narrow-linewidth lasers are vital for a broad range of scientific and technological applications, including atomic clocks and precision sensing. Achieving high frequency stability is often as critical as ensuring scalability, portability, and cost-effectiveness in the development of low noise laser systems. Conventional electro-optic stabilization techniques, such as Pound-Drever-Hall locking to ultra-high-finesse resonators held in a vacuum chamber, provide excellent performance but remain challenging to scale. Here, we propose and experimentally demonstrate a cavity-coupled interferometric laser stabilization technique implemented on a silicon photonic chip and integrated with a compact, scalable micro-Fabry-P\'erot cavity. The vacuum-gap optical cavity operates in air, achieving a quality factor of approximately $2.0\times 10^9$ and a fractional frequency instability of $1.45\times 10^{-12}$ at one-second averaging time. Integration of the proposed technique with the compact cavity yields more than 38-fold reduction in the laser's integrated linewidth and nearly three orders of magnitude suppression of frequency noise at 10 Hz offset frequency. The hybrid-integration of the proposed photonic chip with the micro-Fabry-P\'erot cavity establishes a scalable and portable route toward chip-integrated ultra-stable lasers, paving the way for precision optical systems deployable beyond laboratory environments.