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arXiv:1110.1256 · Physical Review Letters

Driving Rydberg-Rydberg Transitions from a Coplanar Microwave Waveguide

S. D. Hogan, Josef A. Agner, Frédéric Merkt, T. Thiele, Stefan Filipp, Andreas J. Wallraff

Published Feb 9, 2012• 111 citations
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Abstract

The coherent interaction between ensembles of helium Rydberg atoms and microwave fields in the vicinity of a solid-state coplanar waveguide is reported. Rydberg-Rydberg transitions, at frequencies between 25 and 38 GHz, have been studied for states with principal quantum numbers in the range 30-35 by selective electric-field ionization. An experimental apparatus cooled to 100 K was used to reduce effects of blackbody radiation. Inhomogeneous, stray electric fields emanating from the surface of the waveguide have been characterized in frequency- and time-resolved measurements and coherence times of the Rydberg atoms on the order of 250 ns have been determined. These results represent a key element in the development of an experimental architecture to interface Rydberg atoms with solid-state devices.

DOI
10.1103/physrevlett.108.063004

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The coherent interaction between ensembles of helium Rydberg atoms and microwave fields in the vicinity of a solid-state coplanar waveguide is reported. Rydberg-Rydberg transitions, at frequencies between 25 and 38 GHz, have been studied for states with principal quantum numbers in the range 30-35 by selective electric-field ionization. An experimental apparatus cooled to 100 K was used to reduce effects of blackbody radiation. Inhomogeneous, stray electric fields emanating from the surface of the waveguide have been characterized in frequency- and time-resolved measurements and coherence times of the Rydberg atoms on the order of 250 ns have been determined. These results represent a key element in the development of an experimental architecture to interface Rydberg atoms with solid-state devices.
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.
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.
We report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np)2{)}^{2})2P3/2{\mathit{P}}_{3/2}P3/2​(\ensuremath{\Vert}MJ{\mathit{M}}_{\mathit{J}}MJ​\ensuremath{\Vert}=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4--14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-\ensuremath{\mu}s interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-\ensuremath{\mu}s time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ``ionization'' that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ``ionization'' in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ``ionization'' probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.
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 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.