Integrated pulsed optically pumped Rb atomic clock with frequency stability of ${10}^{-15}$

Pulsed optically pumped (POP) Rb atomic clock is considered to be a powerful technique for the Rb atomic clock due to the capability of light-shift mitigation and atomic spectroscopy narrowing. Relevant investigations are conducted over two decades, however, no integrated prototype of such a kind of clock has been reported yet. Here, we present an integrated prototype of the POP Rb atomic clock and quantitatively characterize its physical properties. The atomic clock shows a short-term fractional frequency stability of $2.6\times {10}^{-13}/\sqrt{\tau }$ (where $\tau$ is the averaging time), and comes to $2.3\times {10}^{-15}$ with 40 000 s averaging (drift removed) under atmospheric conditions. Physical effects contributing to the long-term frequency stability are carefully analyzed and cavity-pulling shift is identified as the leading limit. The techniques presented here enable realizing a low ${10}^{-15}$ level vapor-cell atomic clock under atmospheric conditions, which could benefit a wide range of terrestrial applications, such as quantum communication, decimeter-level terrestrial positioning.