  Laser-frequency stabilization with on-chip photonic integrated circuits will
provide compact, low cost solutions to realize spectrally pure laser sources.
Developing high-performance and scalable lasers is critical for applications
including quantum photonics, precision navigation and timing, spectroscopy, and
high-capacity fiber communications. We demonstrate a significant advance in
compact, stabilized lasers to achieve a record low integral emission linewidth
and precision carrier stabilization by combining integrated waveguide nonlinear
Brillouin and ultra-low loss waveguide reference resonators. Using a pair of
56.4 Million quality factor (Q) Si$_3$N$_4$ waveguide ring-resonators, we
reduce the free running Brillouin laser linewidth by over an order of magnitude
to 330 Hz integral linewidth and stabilize the carrier to 6.5$\times$10$^{-13}$
fractional frequency at 8 ms, reaching the cavity-intrinsic thermorefractive
noise limit for frequencies down to 80 Hz. This work demonstrates the lowest
linewidth and highest carrier stability achieved to date using planar, CMOS
compatible photonic integrated resonators, to the best of our knowledge. These
results pave the way to transfer stabilized laser technology from the tabletop
to the chip-scale. This advance makes possible scaling the number of stabilized
lasers and complexity of atomic and molecular experiments as well as reduced
sensitivity to environmental disturbances and portable precision atomic,
molecular and optical (AMO) solutions.
