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We utilize two-photon high-precision microwave spectroscopy of$ng\rightarrow(n+2)g$ transitions to precisely measure thehigh-angular-momentum $g$-series quantum defect of $^{85}$Rb. Samples of coldRydberg atoms in the $ng$ state are prepared via a three-photon opticalexcitation combined with controlled electric-field mixing and probed with40-$\mu$s-long microwave interaction pulses. The leading systematic uncertaintyarises from DC Stark shifts, which is addressed by a cancellation of backgroundelectric fields in all three dimensions. From our measurements and an analysisof systematic uncertainties from DC and AC Stark shifts, van der Waalsinteractions, and microwave frequency calibration, we obtain$\delta_0=0.0039990(21)$ and $\delta_2=-0.0202(21)$. We discuss our results incontext with recent work elsewhere, as well as applications towards precisionmeasurement.

Measurement of Rb g-series quantum defect using two-photon microwave spectroscopy