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

A method for performing a precision measurement of the Rydberg constant R-infinity 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-infinity. 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-infinity in a measurement under the presence of the earth's gravity is 10(-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 Rb+ polarizability (relative-uncertainty contribution of approximate to 3x10(-12)).