Measuring the Rydberg constant using circular Rydberg atoms in an intensity-modulated optical lattice

Abstract

A method for performing a precision measurement of the Rydberg constant ${R}_{\ensuremath{\infty}}$ using cold circular Rydberg atoms is proposed. These states have long lifetimes as well as negligible quantum electrodynamics and no nuclear-overlap corrections. Due to these advantages, the measurement can help solve the proton radius puzzle [J. C. Bernauer and R. Pohl, Sci. Am. 310, 32 (2014)]. The atoms are trapped using a Rydberg-atom optical lattice and transitions are driven using a recently demonstrated lattice-modulation technique to perform Doppler-free spectroscopy. The circular-state transition frequency yields ${R}_{\ensuremath{\infty}}$. Laser wavelengths and beam geometries are selected such that the lattice-induced transition shift is minimized. The selected transitions have no first-order Zeeman and Stark corrections, leaving only manageable second-order Zeeman and Stark shifts. For Rb, the projected relative uncertainty of ${R}_{\ensuremath{\infty}}$ in a measurement under the presence of the earth's gravity is ${10}^{\ensuremath{-}11}$, with the main contribution coming from the residual lattice shift. This could be reduced in a future microgravity implementation. The next-important systematic uncertainty arises from the ${\mathrm{Rb}}^{+}$ polarizability (relative-uncertainty contribution of $\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$).