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

Abstract

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