  Microresonator-based soliton frequency combs - microcombs - have recently
emerged to offer low-noise, photonic-chip sources for optical measurements.
Owing to nonlinear-optical physics, microcombs can be built with various
materials and tuned or stabilized with a consistent framework. Some
applications require phase stabilization, including optical-frequency synthesis
and measurements, optical-frequency division, and optical clocks. Partially
stabilized microcombs can also benefit applications, such as oscillators,
ranging, dual-comb spectroscopy, wavelength calibration, and optical
communications. Broad optical bandwidth, brightness, coherence, and frequency
stability have made frequency-comb sources important for studying comb-matter
interactions with atoms and molecules. Here, we explore direct microcomb atomic
spectroscopy, utilizing a cascaded, two-photon 1529-nm atomic transition of
rubidium. Both the microcomb and the atomic vapor are implemented with planar
fabrication techniques to support integration. By fine and simultaneous control
of the repetition rate and carrier-envelope-offset frequency of the soliton
microcomb, we obtain direct sub-Doppler and hyperfine spectroscopy of the
$4^2D_{5/2}$ manifold. Moreover, the entire set of microcomb modes are
stabilized to this atomic transition, yielding absolute optical-frequency
fluctuations of the microcomb at the kilohertz-level over a few seconds and < 1
MHz day-to-day accuracy. Our work demonstrates atomic spectroscopy with
microcombs and provides a rubidium-stabilized microcomb laser source, operating
across the 1550 nm band for sensing, dimensional metrology, and communication.
