Precision Measurements with Rydberg States of Rubidium

Rydberg atoms can be excellent tools for precision metrology thanks to their long lifetimes and interactions with external fields and other atoms that scale with large powers of the principal quantum number. In this thesis I present a detailed description and characterization of an experimental setup I built to perform precision measurements with Rydberg atoms. In particular, this machinery was constructed to perform a precision measurement of the Rydberg constant using circular Rydberg atoms for which I also calculate and describe the expected sources of systematic uncertainties and how to manage them. Moreover, in this thesis I present precision measurements of the rubidium-85 nS hyperfine structure (HFS) splittings. Circular states are chosen for the precision measurement of the Rydberg constant because they have longer lifetimes than low-l Rydberg atoms, negligible quantum-electrodynamics(QED) and no nuclear-overlap corrections. Due to these advantages, the measurement can help solve the "proton radius puzzle", which has cast doubts on the values of the proton radius and the Rydberg constant. In the pursued experiment, the atoms are trapped using a ponderomotive optical lattice, and transitions are driven using a recently-demonstrated lattice-modulation technique to perform Doppler-free spectroscopy. These methods allow us to exploit the long lifetime of the circular states while also yielding the necessary narrow linewidths. The circular-state transition frequency yields the Rydberg constant, after accounting for systematics. 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 the Rydberg constant in a measurement under the presence of the Earth’s gravity is in the order of one part ten parts in a trillion, with the main contribution coming from the residual lattice shift. This could be reduced in a future micro-gravity implementation. I perform a precision measurement of the HFS splitting in rubidium-85. The splittings between the F=2 and F=3 of nS atomic levels are obtained by driving microwave transitions between nP and nS atomic levels for n=43 to 46. From the splittings the HFS constant is determined to be 15.37(17) GHz which is almost an order of magnitude improvement in precision from the value available in the literature. These experiments also prove the capabilities of the experimental setup built to measure the Rydberg constant.