Photonic chip for laser stabilization to an atomic vapor at a precision of $10^{-11}$

We perform precision spectroscopy of rubidium confined in a micro-machined, 27~mm$^3$ volume, vapor cell using a collimated free space 120~$\bm{\mu}$m diameter laser beam derived directly from a single mode silicon nitride waveguide. With this optical-fiber integrated photonic spectrometer, with total volume of less than 1~cm$^3$, we demonstrate an optical frequency reference at 780~nm with a precision of $\bm{10^{-11}}$ from 1 to $\bm{10^4}$ seconds. The ability to leverage the benefits of both photonic integration and precision spectroscopy with this device will be an enabling technology for the next generation of quantum sensors and devices based on atomic vapors.