  Today's state of the art precision experiments in quantum, gravimetry,
navigation, time keeping, and fundamental science have strict requirements on
the level and spectral distribution of laser frequency noise. For example, the
laser interaction with atoms and qubits requires ultra-low frequency noise at
multiple offset frequencies due to hyperfine atomic transitions, motional
sidebands, and fast pulse sequencing. Chip-scale integration of lasers that
meet these requirements is essential for reliability, low-cost, and weight.
Here, we demonstrate a significant advancement in atomic precision light
sources by realizing a chip-scale, low-cost, 780 nm laser for rubidium atom
applications with record-low 640 mHz (white noise floor at 0.2 Hz$^2$/Hz)
fundamental and 732 Hz integral linewidths and a frequency noise that is
multiple orders of magnitude lower than previous hybrid and heterogeneous
self-injection locked 780 nm lasers and lower noise than bulk microresonator
implementations. The laser is a Fabry-P\'erot laser diode self-injection locked
to an ultra-high Q photonic integrated silicon nitride resonator. This
performance is enabled by a 145 million resonator Q with a 30 dB extinction
ratio, the highest Q at 780 nm, to the best of our knowledge. We analyze the
impact of our frequency noise on specific atomic applications including atomic
frequency references, Rydberg quantum gates, and cold atom gravimeters. The
photonic integrated resonator is fabricated using a CMOS foundry-compatible,
wafer-scale process, with demonstrated integration of other components showing
promise for a full system-on-a-chip. This performance is scalable to other
visible atomic wavelengths, opening the door to a variety of transitions across
many atomic species and enabling low-power, compact, ultra-low noise lasers
impacting applications including quantum sensing, computing, clocks and more.
