An optical atomic clock using $4D_J$ states of rubidium

We analyze an optical atomic clock using two-photon $5S_{1/2} \rightarrow 4D_J$ transitions in rubidium. Four one- and two-color excitation schemes to probe the fine-structure states $4D_{3/2}$ and $4D_{5/2}$ are considered in detail. We compare key characteristics of Rb $4D_J$ and $5D_{5/2}$ two-photon clocks. The $4D_J$ clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a "magic" wavelength near 1060~nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the $10^{-13}/\sqrt{\tau(s)}$-level, with integration time $\tau$ in seconds, and a relative accuracy of $\sim 10^{-13}$. We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550~nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb $4D_J$-states.