Measurement of the Rb <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi></mml:math>-series quantum defect using two-photon microwave spectroscopy

Abstract

We utilize two-photon, high-precision microwave spectroscopy of $ng\ensuremath{\rightarrow}(n+2)g$ transitions to precisely measure the high-angular-momentum $g$-series quantum defect of $^{85}\mathrm{Rb}$. Samples of cold Rydberg atoms in the $ng$ state are prepared via a three-photon optical excitation combined with controlled electric-field mixing and probed with 40-$\ensuremath{\mu}\mathrm{s}$-long microwave interaction pulses. The leading systematic uncertainty arises from DC Stark shifts, which is addressed by a cancellation of background electric fields in all three dimensions. From our measurements and an analysis of systematic uncertainties from DC and AC Stark shifts, van der Waals interactions, and microwave frequency calibration, we obtain ${\ensuremath{\delta}}_{0}=0.003\phantom{\rule{0.16em}{0ex}}999\phantom{\rule{0.16em}{0ex}}0(21)$ and ${\ensuremath{\delta}}_{2}=\ensuremath{-}0.0202(21)$. We discuss our results in context with recent work elsewhere, as well as applications towards precision measurement.