  Atomic beams are a longstanding technology for atom-based sensors and clocks
with widespread use in commercial frequency standards. Here, we report the
demonstration a chip-scale microwave atomic beam clock using coherent
population trapping (CPT) interrogation in a passively pumped atomic beam
device. The beam device consists of a hermetically sealed vacuum cell
fabricated from an anodically bonded stack of glass and Si wafers. Atomic beams
are created using a lithographically defined microcapillary array connected to
a Rb reservoir1 and propagate in a 15 mm long drift cavity. We present a
detailed characterization of the atomic beam performance (total Rb flux
$\approx 7.7 \times 10^{11} s^{-1}$ at 363 K device temperature) and of the
vacuum environment in the device (pressure < 1 Pa), which is sustained using
getter materials which pump residual gases and Rb vapor. A chip-scale beam
clock is realized using Ramsey CPT spectroscopy of the 87Rb ground state
hyperfine transition over a 10 mm Ramsey distance in the atomic beam device.
The prototype atomic beam clock demonstrates a fractional frequency stability
of $\approx 1.2 \times 10^{-9}/\sqrt{\tau}$ for integration times $\tau$ from 1
s to 250 s, limited by detection noise. Optimized atomic beam clocks based on
this approach may exceed the long-term stability of existing chip-scale clocks,
and leading long-term systematics are predicted to limit the ultimate
fractional frequency stability below $10^{-12}$.
