Two-photon Doppler-free spectroscopy of the $6s^2{}^1{S}_0\to 6s23s{}^1{S}_0$ Rydberg transition for quantum sensing in ytterbium

Here we report atomic structure calculations and experimental observations of the two-photon $6s^2{}^1{S}_0\to 6s23s{}^1{S}_0$ transition in Yb. The unique level structure of Yb places the $6s6p{}^1{P}_1$ state’s energy at $\approx \text{\hspace{0.17em}⁣}49.7\mathrm{\%}$ of the ionization energy, which facilitates two-photon Doppler-free excitation of the $6s23s{}^1{S}_0$ Rydberg state from the $6s^2{}^1{S}_0$ ground state at a relatively low optical intensity. This $J=0\to J=0$ transition is immune to first-order Zeeman and electric quadrupole shifts, has reduced sensitivity to higher-order Zeeman shifts, and is further predicted to have relatively low sensitivity to density shifts. Using configuration interaction theory, we compute relevant properties of the $6s23s{}^1{S}_0$ Rydberg state for sensing, including the $C_6$ coefficient, dc polarizability, blackbody radiation (BBR) shift, and BBR depopulation rate. As a first experimental step, we demonstrate two-photon Doppler-free spectroscopy of the $6s^2{}^1{S}_0\to 6s23s{}^1{S}_0$ transition. From our experimental spectra, we estimate the natural linewidth (lifetime) of the $6s23s{}^1{S}_0$ state to be 90 kHz (1.8 $\mu$s). We believe this transition, or other $6s^2{}^1{S}_0\to 6sns{}^1{S}_0$ transitions in Yb with $n\approx 23$, may find use in a variety of sensing applications, potentially including a two-photon clock, electrometer, or BBR thermometer.