Electrometry of a single resonator mode at a Rydberg-atom–superconducting-circuit interface

The electric-field distribution in a single mode of $\ensuremath{\lambda}/4$ superconducting coplanar waveguide (CPW) microwave resonator has been probed using beams helium Rydberg atoms. In the experiments atoms were prepared $1\mathrm{s}55\mathrm{s}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{S}}_{1}$ level by laser photoexcitation. They then traveled over CPW that was fabricated on NbN chip operated at 3.8 K. driven its third-harmonic frequency, near resonant with two-photon $1\mathrm{s}55\mathrm{s}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{S}}_{1}\ensuremath{\rightarrow}1\mathrm{s}56\mathrm{s}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{S}}_{1}$ transition ${\ensuremath{\omega}}_{55\mathrm{s},\phantom{\rule{0.16em}{0ex}}56\mathrm{s}}/2=2\ensuremath{\pi}\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}19.556\phantom{\rule{0.16em}{0ex}}499$ GHz. coherence times atom--resonator-field interaction determined selected locations above time-domain measurements Rabi oscillations and found to be up $0.8\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$ for frequencies $\ensuremath{\sim}2\ensuremath{\pi}\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}3$ MHz. atomic superposition states, generated following field resonator, inferred from high-resolution cavity-enhanced Ramsey spectra $\ensuremath{\sim}2.5\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$. These also allowed measurement residual uncanceled dc electric fields $26.6\ifmmode\pm\else\textpm\fi{}0.6$ mV/cm position $\ensuremath{\sim}300\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ surface chip. results represent an essential step toward applications hybrid systems, comprising coherently coupled circuits, quantum optics information processing.