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Nature volume 615, pages 614–619 (2023 )Cite this article
Early experiments with transiting circular Rydberg atoms in a superconducting resonator laid the foundations of modern cavity and circuit quantum electrodynamics1, and helped explore the defining features of quantum mechanics such as entanglement. Whereas ultracold atoms and superconducting circuits have since taken rather independent paths in the exploration of new physics, taking advantage of their complementary strengths in an integrated system enables access to fundamentally new parameter regimes and device capabilities2,3. Here we report on such a system, coupling an ensemble of cold 85Rb atoms simultaneously to an, as far as we are aware, first-of-its-kind optically accessible, three-dimensional superconducting resonator4 and a vibration-suppressed optical cavity in a cryogenic (5 K) environment. To demonstrate the capabilities of this platform, and with an eye towards quantum networking5, we leverage the strong coupling between Rydberg atoms and the superconducting resonator to implement a quantum-enabled millimetre wave (mmwave) photon to optical photon transducer6. We measured an internal conversion efficiency of 58(11)%, a conversion bandwidth of 360(20) kHz and added thermal noise of 0.6 photons, in agreement with a parameter-free theory. Extensions of this technique will allow near-unity efficiency transduction in both the mmwave and microwave regimes. More broadly, our results open a new field of hybrid mmwave/optical quantum science, with prospects for operation deep in the strong coupling regime for efficient generation of metrologically or computationally useful entangled states7 and quantum simulation/computation with strong non-local interactions8.
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Due to the proprietary format of the experimental data as collected for this manuscript, these are available from the corresponding author on request.
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Funding for this research was provided by the National Science Foundation (NSF) through QLCI-HQAN grant no. 2016136, by the Army Research Office through MURI grant no. W911NF2010136 and by the Air Force Office of Scientific Research through MURI grant no. FA9550-16-1-0323. It was also supported by the University of Chicago Materials Research Science and Engineering Center, which is funded by the NSF under award no. DMR-1420709. M.S. acknowledges support from the NSF GRFP. We acknowledge E. Riis and P. Griffin for fabrication of the grating used for our cryogenic MOT.
These authors contributed equally: Aishwarya Kumar, Aziza Suleymanzade, Mark Stone
The Department of Physics, The James Franck Institute and The Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA
Aishwarya Kumar, Aziza Suleymanzade, Mark Stone, Lavanya Taneja, Alexander Anferov, David I. Schuster & Jonathan Simon
The Department of Physics, Stanford University, Stanford, CA, USA
Aishwarya Kumar & Jonathan Simon
The Department of Applied Physics, Stanford University, Stanford, CA, USA
David I. Schuster & Jonathan Simon
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The experiments were designed by A.K., A.S., M.S., L.T., D.I.S. and J.S. The apparatus was built by A.K., A.S., M.S. and L.T. Collection of data was handled by A.K. and L.T. All authors analysed the data and contributed to the manuscript.
The authors declare no competing interests.
Nature thanks David Petrosyan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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a, Cryogenic 85Rb trap. The atoms are emitted from a dispenser source mounted at room temperature, propagate through a small aperture at the back of the grating towards the capture volume of the grating MOT. The Helmholtz coils and all supporting structures are thermalized to 40K. b, Millimeter wave circuit used for characterizing the superconducting cavity and sending in mmwave photons for the interconversion experiment. Most of the power from the “science” source is diverted towards a power detector, which is used to actively stabilize the mmwave power using a voltage controlled attenuator (VCA). Both the science and the tuning sources are equipped with rf-switches to fully extinguish any signal to the cavity. c, The custom two-chambered 4K cryogenic system built for our hybrid cavity-QED experiments.
a, The levels and light polarizations involved in transduction. The mmwave cavity (green) science mode is linearly polarized along the optical cavity (red) direction. We choose (through a magnetic field and optical pumping) the quantization axis along the lattice beam direction to achieve phase matching and zero angular momentum change on a round trip at the same time. The mmwave mode polarization, which is orthogonal to this quantization axis, can be decomposed as a linear combination of σ+ and σ− polarizations. The UV beam (purple) is linearly polarized orthogonal to both the lattice direction and the optical cavity axis, and thus can also be decomposed as a linear combination of σ+ and σ− polarizations. The 481 nm beam and the 780 nm probe (or the emitted interconverted photon) are linearly polarized along the lattice direction, and therefore have π polarization with respect to the quantization axis. We start by optically pumping to the stretched hyperfine magnetic sublevel, which results in the UV σ+ component and the mmwave σ− component not coupling to any available state. The effect of the Raman couplings generated from these polarizations is suppressed due to the magnetic field lifting the degeneracy. b, Reflection measurement off of the port of the optical cavity at which the photons are counted for any of our experiments described in the main text. The minimum reflection point directly yields (\(1-2{\kappa }_{{opt}}^{{ext}}/{\kappa }_{{opt}}\) )2. The gray line is a model fit, with slight deviations due to a small polarization splitting of the cavity, and polarization impurity of the probe. c, “In-situ” measurement of the mmwave cavity spectrum using the shift of the dark polariton/EIT resonance. The atomic transition is far-detuned (2π × 12.4 MHz) from the cavity and a mmwave drive is scanned in frequency around the cavity resonance. The resulting ac-Stark shift of the dark polariton is porportional to the mmwave power in cavity. The gray line is a fit to a Lorentzian modified to account for the effect of the changing detuning of the drive from the atoms.
a, The calculated ac Stark shifts of the 36S1/2 and 35P1/2 “science” states as the power in the 101.318 GHz “tuning” mode of the cavity is increased. The tuning of the atomic states allows us to control the detuning (∆) between the atomic transition and the mmwave cavity for transduction, as well as other experiments like those in Fig. 2c. b, As we vary the classical drive on tuning mode, we measure the shifts of the 36S1/2 and 35P1/2 states using a cavity Rydberg EIT and direct UV spectroscopy from the 5S1/2 state, respectively. This calibration then allows us to infer the 35P1/2 shift (which is more involved to measure day-to-day) from the 36S1/2 shift measured via cavity Rydberg EIT. We find excellent agreement between our calculation and the observed shifts.
a, Same data as Fig. 2c, but the full data set with spectra at additional atom-mmwave cavity detunings (∆ in main text), which were omitted from the plot in the main text for clarity. For this dataset, we simply varied the strength of the “tuning” field to shift the atomic states, but did not change the 481 nm frequency – which would be required to keep the dark polariton at the same frequency as the optical cavity (at ∆probe = 0 MHz). The asymmetry arises because at the point which the mmwave atomic transition is resonant with the mmwave cavity, the optical cavity and 481 nm beam are not resonant with the 5S1/2 ↔ 36S1/2 transition. b, Master equation simulation of the data in a, using the non-linear Hamiltonian derived in SI B (equation S8), where all the parameters were experimentally measured using spectra with and without the 481 nm beam at a large ∆. This excludes gmm and the number of thermal photons, which were calculated from first principles. In both a and b, the solid lines are Lorentzian fits. c, The linewidths obtained from the Lorentzian fits of both theory and experiment. We find excellent agreement between the two, building confidence in our model. The dark polariton starts to broaden again near the edges because of mixing with the bright polaritons.
a, Left - Measured dark polariton/Rydberg EIT spectra as the “science” mode drive strength is increased at an atom-mmwave cavity detuning, ∆ = 2π × 1.4 MHz. We first measure a reference spectrum with the mmwave source entirely turned off using an rf-switch (orange). An actively locked mmwave drive (using a power detector and a VCA, see Methods A, Extended Data Fig. 1) is then applied with increasing strength (light blue to dark blue). The solid lines are Lorentzian fits. Right - The extracted shifts by fitting the spectra in the left panel as the lock set point is increased. Note that even at the lowest lock set-point, there is some leakage from the VCA, which necessitates measuring the orange reference in the left panel with no mmwave power from the source. After a threshold, the shifts saturate because the VCA reaches lowest attenuation and there is no more mmwave drive power available. b, Master equation calculation of the data in a using the non-linear Hamiltonian given by equation 4 with parameters independently measured or calculated from first principles (gmm and number of thermal photons) and an added coherent drive. This calculation allows us to calibrate our coherently driven photon number (nph) and the dispersive shift of the EIT resonance. Left - The calculated spectra with Lorentzian fits. Right - The shift of the EIT resonance against the number of mmwave photons driven into the cavity by the coherent drive in steady state. The simple first order expression (red) over-estimates the shifts. We instead calculate and use a much more accurate analytical result (green) in SI C.
This file contains Supplementary Figs. 1–4, text sections A–F, maths and references.
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Kumar, A., Suleymanzade, A., Stone, M. et al. Quantum-enabled millimetre wave to optical transduction using neutral atoms. Nature 615, 614–619 (2023). https://doi.org/10.1038/s41586-023-05740-2
DOI: https://doi.org/10.1038/s41586-023-05740-2
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