Controlling light shifts in chip-scale atomic beam clocks
Chip-scale atomic beam clocks are being investigated to extend the range of clock stability achievable in low-power timing applications. Here, we demonstrate a centimeter-scale, Ramsey coherent population trapping (CPT) clock based on a microfabricated Cs atomic beam device and investigate the interplay between light shifts and Doppler shifts that determines its leading clock systematics. We show that these shifts exhibit competing dependencies on CPT light parameters, leading to ``doubly-insensitive" operating points where the clock frequency is simultaneously insensitive to laser frequency and power. We further demonstrate a method for controlling key clock shifts using spectroscopic signatures from the atomic beam that is compatible with fully-integrated operation. The clock achieves a fractional frequency stability of $2 \times 10^{-10}$ at $1~\textrm{s}$ and sub-$\mu$s drift over nearly $17~\textrm{hours}$, with leading CPT light systematics controlled below the $10^{-12}$ level.