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Measurement of the Rydberg Constant with Trapped Rydberg Atoms

A measurement of the Rydberg constant using cold circular Rydberg atoms is proposed. Since these atoms have long lifetimes, negligible quantum electrodynamics and no nuclear-overlap corrections, the measurement can shed new light on the “proton radius puzzle”. The atoms are trapped in an optical lattice. Transitions are driven using a lattice-modulation technique to perform Doppler-free sub-THz spectroscopy; the transition frequencies yield the Rydberg constant. The selected transitions are free of first-order Zeeman and Stark shifts. Systematic uncertainties due to lattice-induced shifts, core-polarization, second-order Zeeman and Stark shifts, etc are estimated.