# Measuring the Rydberg Constant Using Circular Rydberg Atoms in an Intensity-Modulated Optical Lattice

## TL;DR

This paper proposes a novel method to measure the Rydberg constant precisely using cold circular Rydberg atoms in an optical lattice, potentially resolving the proton radius puzzle with high accuracy.

## Contribution

It introduces a new experimental approach employing lattice-modulation spectroscopy with circular Rydberg atoms to improve the precision of Rydberg constant measurements.

## Key findings

- Projected relative uncertainty of 10^{-11} for R_infinity in Earth's gravity.
- Minimized lattice-induced transition shifts and systematic corrections.
- Potential for further uncertainty reduction in micro-gravity environments.

## Abstract

A method for performing a precision measurement of the Rydberg constant, $R_{\infty}$, using cold circular Rydberg atoms is proposed. These states have long lifetimes, as well as negligible quantum-electrodynamics (QED) and no nuclear-overlap corrections. Due to these advantages, the measurement can help solve the "proton radius puzzle" [Bernauer, 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 $R_{\infty}$. 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 $R_{\infty}$ 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 micro-gravity implementation. The next-important systematic arises from the Rb$^+$ polarizability (relative-uncertainty contribution of $\approx 3 \times10^{-12}$).