532-nm intensity-modulated optical lattice for driving Rydberg-Rydberg transitions

We present progress towards implementing an experiment to make a precision measurement of the Rydberg constant using circular-state Rydberg atoms. An independent measurement of the Rydberg constant will contribute to solving discrepancies in fundamental physics, most notably the ``proton radius puzzle'' [1]. The experiment relies on driving a circular to near-circular, n $=$ 51 to 53 Rydberg-Rydberg transition.~This transition was chosen because it is insensitive to nuclear charge distribution and first-order Stark and Zeeman effects, yielding less uncertainty in a Rydberg constant measurement. The Rydberg atoms are trapped in a 532-nm~optical lattice, which is intensity-modulated so that its temporal harmonics drive the microwave-frequency transitions, so-called ``ponderomotive spectroscopy.'' We have previously demonstrated ponderomotive spectroscopy using 1064-nm~light modulated by a fiber-based electro-optic modulator (EOM) [2]. Here, the 532-nm light offers the benefit of a ``magic wavelength'' for the transition. Finding a method to prepare a tunable, high-power, intensity-modulated optical lattice at 532 nm presents a substantial challenge. Here, we report on progress in overcoming this challenge as well as on other recent experimental developments.\\[4pt] [1] R. Pohl, et al., Nature, 466, 213 (2010).\\[0pt] [2] K.R. Moore, S.E. Anderson, G. Raithel, Nat. Commun., 6 (2015).