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arXiv:2508.20292 · Physical Review A

Interfacing Rydberg atoms with a chip-based superconducting microwave resonator using an ac-Stark-shifted single-photon transition

L. L. Brown, I. K. Bhangoo, S. D. Hogan

Published Dec 17, 2025• 1 citation
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Abstract

Helium atoms in the 1 s 50 s S 1 3 Rydberg level have been resonantly coupled to the 2 π × 11.722 GHz second harmonic mode of a chip-based superconducting coplanar wave-guide microwave resonator. To achieve this, the single-photon electric-dipole-allowed 1 s 50 s S 1 3 → 1 s 50 p P J 3 transition was tuned into resonance with the resonator mode through the ac Stark shift induced by a second strong 2 π × 3.350 GHz microwave dressing field. The effects of this dressing field, and residual uncanceled dc electric fields at the location of the atoms close to the superconducting chip surface were interpreted with support from Floquet calculations of the energy level structure of the Rydberg states. To observe appreciable population transfer in the 1 µ s atom-resonator interaction time using this transition, which had an electric dipole moment of 1500 e a 0 , pulsed microwave fields were injected into the resonator. From the photon occupation number in the resonator mode under these conditions, the single-photon Rabi frequency associated with the coupling of the atoms to the resonator was estimated to be ∼ 2 π × 100 Hz . These results represent an important step toward operation of this Rydberg-atom–superconducting-circuit interface in the single-photon strong-coupling regime.

DOI
10.1103/hzd4-1x22

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Helium atoms in the 1 s 50 s S 1 3 Rydberg level have been resonantly coupled to the 2 π × 11.722 GHz second harmonic mode of a chip-based superconducting coplanar wave-guide microwave resonator. To achieve this, the single-photon electric-dipole-allowed 1 s 50 s S 1 3 → 1 s 50 p P J 3 transition was tuned into resonance with the resonator mode through the ac Stark shift induced by a second strong 2 π × 3.350 GHz microwave dressing field. The effects of this dressing field, and residual uncanceled dc electric fields at the location of the atoms close to the superconducting chip surface were interpreted with support from Floquet calculations of the energy level structure of the Rydberg states. To observe appreciable population transfer in the 1 µ s atom-resonator interaction time using this transition, which had an electric dipole moment of 1500 e a 0 , pulsed microwave fields were injected into the resonator. From the photon occupation number in the resonator mode under these conditions, the single-photon Rabi frequency associated with the coupling of the atoms to the resonator was estimated to be ∼ 2 π × 100 Hz . These results represent an important step toward operation of this Rydberg-atom–superconducting-circuit interface in the single-photon strong-coupling regime.
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 1s55s3S11\mathrm{s}55\mathrm{s}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{S}}_{1}1s55s3S1​ 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.
Microwave-dressed Rydberg atoms in pairs of states that are optically accessible and engineered so that the frequency of the transition between them is tunable while exhibiting a low sensitivity to stray electric fields have been interfaced with a superconducting coplanar waveguide (CPW) microwave resonator. This was achieved with helium atoms in triplet Rydberg states with principal quantum numbers n = 55 and 56. The atoms were dressed with two strong microwave fields—a control field and a differential polarizability nulling field. The control field allowed the atoms to be coupled to the resonator using the two-color two-photon transition between the equal parity 1 s 55 s S 1 3 ≡ | 55 s 〉 and 1 s 56 s S 1 3 ≡ | 56 s 〉 Rydberg states, with one photon supplied by it and the other provided by the resonator. The nulling field was detuned from the field-free 1 s 55 s S 1 3 → 1 s 55 p P J 3 ≡ | 55 p 〉 transition to admix | 55 p 〉 character into the | 55 s 〉 state and eliminate the differential static electric dipole polarizability of the | 55 s 〉 and | 56 s 〉 states. The experiments were performed with atoms located ∼ 300 µ m above a λ / 4 niobium nitride superconducting CPW resonator operated at temperatures between 3.59 and 3.73 K . The measured ac and dc Stark shifts of the Rydberg states at this atom-circuit interface in the presence of the dressing fields are in good quantitative agreement with the results of Floquet calculations. The differential polarizability nulling fields used in the experiments allowed the difference in the Stark shifts of the | 55 s 〉 and | 56 s 〉 states over the range of dc fields offset from the residual stray field by ± 65 mV/cm to be reduced from 2 π × 2.1 MHz to 2 π × 125 kHz. Published by the American Physical Society 2024
The coherent interaction of Rydberg helium atoms with microwave fields in a λ/4 superconducting coplanar waveguide resonator has been exploited to probe the spectral characteristics of an individual resonator mode. This was achieved by preparing the atoms in the 1s55s 3S1 Rydberg level by resonance enhanced two-color two-photon excitation from the metastable 1s2s 3S1 level. The atoms then traveled over the resonator in which the third harmonic microwave field, at a frequency of ωres=2π×19.556 GHz, drove the two-photon 1s55s 3S1 → 1s56s 3S1 transition. By injecting a sequence of Ramsey pulses into the resonator and monitoring the coherent evolution of the Rydberg state population by state-selective pulsed electric field ionization as the frequency of the microwave field was tuned, spectra were recorded that allowed the resonator resonance frequency and quality factor to be determined with the atoms acting as microscopic quantum sensors.
The coherent interaction of Rydberg helium atoms with microwave fields in a λ/4 superconducting coplanar waveguide resonator has been exploited to probe the spectral characteristics of an individual resonator mode. This was achieved by preparing the atoms in the 1s55s 3S1 Rydberg level by resonance enhanced two-color two-photon excitation from the metastable 1s2s 3S1 level. The atoms then traveled over the resonator in which the third harmonic microwave field, at a frequency of ωres=2π×19.556 GHz, drove the two-photon 1s55s 3S1 → 1s56s 3S1 transition. By injecting a sequence of Ramsey pulses into the resonator and monitoring the coherent evolution of the Rydberg state population by state-selective pulsed electric field ionization as the frequency of the microwave field was tuned, spectra were recorded that allowed the resonator resonance frequency and quality factor to be determined with the atoms acting as microscopic quantum sensors.
Hybrid quantum systems involving cold atoms and microwave resonators can enable cavity-mediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave-to-optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric-dipole transitions. Here we report on the experimental realization of coherent coupling of a Rydberg transition of ultracold atoms, trapped on an integrated superconducting atom chip, to the microwave field of an on-chip coplanar waveguide resonator. Close to the chip surface, stray electric fields lead to inhomogeneous Rydberg level shifts, which would hinder coherent interactions of atoms in a cloud with the Rydberg excitation lasers and the microwave cavity field. We, however, use optical excitation of a Rydberg state of atoms in a narrow layer with nearly constant electric field, which allows for resonant coupling of the atoms to the cavity microwave field on an appropriate Rydberg transition. We also achieve state-selective detection of the energetically close Rydberg states. We then observe and characterize cavity-driven Rabi oscillations between a pair of atomic Rydberg states. The residual damping of the oscillations is dominated by the spread of Rabi frequencies of atoms in different positions of the resonant cavity mode, as revealed by our model. Despite the technical challenges, our studies demonstrate the feasibility of coherent-state manipulation of Rydberg atoms interacting with superconducting circuits, paving the way for realization of capable hybrid quantum systems.
Rydberg helium atoms traveling in pulsed supersonic beams have been coupled to microwave fields in a superconducting coplanar waveguide (CPW) resonator. The atoms were initially prepared in the 1s55s ^{3}S_{1} Rydberg level by two-color two-photon laser excitation from the metastable 1s2s ^{3}S_{1} level. Two-photon microwave transitions between the 1s55s ^{3}S_{1} and 1s56s ^{3}S_{1} levels were then driven by the 19.556 GHz third-harmonic microwave field in a quarter-wave CPW resonator. This superconducting microwave resonator was fabricated from niobium nitride on a silicon substrate and operated at temperatures between 3.65 and 4.30 K. The populations of the Rydberg levels in the experiments were determined by state-selective pulsed electric field ionization. The coherence of the atom-resonator coupling was studied by time-domain measurements of Rabi oscillations.