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Optically heralded microwave photon addition

Nature Physics volume 19, pages 1423–1428 (2023)Cite this article

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Abstract

Photons with optical frequencies of a few hundred terahertz are perhaps the only way to distribute quantum information over long distances. Superconducting qubits, which are one of the most promising approaches for realizing large-scale quantum machines, operate on microwave photons at frequencies that are ~40,000 times lower. To network these quantum machines across appreciable distances, we must bridge this frequency gap. Here we implement and demonstrate a transducer that can generate correlated optical and microwave photons. We use it to show that by detecting an optical photon we generate an added microwave photon with an efficiency of ~35%. Our device uses a gigahertz nanomechanical resonance as an intermediary, which efficiently couples to optical and microwave channels through strong optomechanical and piezoelectric interactions. We show continuous operation of the transducer with 5% frequency conversion efficiency, input-referred added noise of ~100, and pulsed microwave photon generation at a heralding rate of 15 Hz. Optical absorption in the device generates thermal noise of less than two microwave photons. Improvements of the system efficiencies and device performance are necessary to realize a high rate of entanglement generation between distant microwave-frequency quantum nodes, but these enhancements are within reach.

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Fig. 1: Transducer schematics and implementation.
Fig. 2: Transducer characterization.
Fig. 3: Optically heralded microwave photon addition.

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Data availability

The data for Figs. 2 and 3 and Extended Data Figs. 1, 2, 3 and 5 are available on Zenodo at https://doi.org/10.5281/zenodo.7903643. Additional data that support the findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

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Acknowledgements

W.J. and F.M.M. thank C. J. Sarabalis and H. Xiong for helpful discussions. A.-H.S.N. acknowledges useful discussions with O. Painter, C. Regal, K. Lehnert, M. Fejer and S. Groeblacher. The authors thank K. K. S. Multani, A. Y. Cleland, O. A. Hitchcock, C. Langrock, B. Kuyken, T. Vandekerckhove and M. P. Maksymowych for fabrication assistance, K. A. Villegas Rosales and N. Drucker at Quantum Machines and Y. Guo for technical support, and K. Serniak and W. D. Oliver at MIT Lincoln Laboratory for providing the TWPA. This work was primarily supported by the US Army Research Office (ARO) Cross-Quantum Systems Science & Technology (CQTS) programme (grant no. W911NF-18-1-0103), the National Science Foundation CAREER award no. ECCS-1941826, the Airforce Office of Scientific Research (AFOSR) (MURI no. FA9550-17-1-0002 led by CUNY) and the David and Lucille Packard Fellowship. Device fabrication was performed at the Stanford Nano Shared Facilities (SNSF) and the Stanford Nanofabrication Facility (SNF), supported by NSF award ECCS-2026822. A.H.S.-N. acknowledges support via a Sloan Fellowship. We also thank NTT Research and Amazon Web Services Inc. for their financial support. Some of this work was funded by the US Department of Energy through grant no. DE-AC02-76SF00515 and via the Q-NEXT Center.

Author information

Author notes

  1. Raphaël Van Laer

    Present address: Department of Microtechnology and Nanoscience, Chalmers University of Technology, Gothenburg, Sweden

  2. These authors contributed equally: Wentao Jiang, Felix M. Mayor.

Authors and Affiliations

  1. Department of Applied Physics and Ginzton Laboratory, Stanford University, Stanford, CA, USA

    Wentao Jiang, Felix M. Mayor, Sultan Malik, Raphaël Van Laer, Timothy P. McKenna, Rishi N. Patel, Jeremy D. Witmer & Amir H. Safavi-Naeini

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Contributions

W.J. designed the device with assistance from F.M.M. and S.M. W.J. and F.M.M. fabricated the device assisted by S.M. W.J., F.M.M. and R.V.L. developed the fabrication process. W.J. and F.M.M. measured the device with assistance from S.M. R.N.P., T.P.M., J.D.W. and A.H.S.-N. provided assistance with the measurement set-up. W.J., F.M.M. and A.H.S.-N. wrote the manuscript with input from all authors. A.H.S.-N. supervised the project.

Corresponding author

Correspondence to Amir H. Safavi-Naeini.

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A.H.S.-N. is an Amazon Scholar. The other authors declare no competing interests.

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Nature Physics thanks Christophe Galland and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Microwave high-impedance waveguide characterization.

a, Schematics of the high impedance (high-Z) waveguide. The mechanical external coupling is approximately proportional to the impedance of the environment. Thus the effective impedance Zeff looking from the mechanics side into the high-Z waveguide gives us intuition on the enhanced external coupling. b, Calculated Zeff and the group delay with a free spectral range of 110 MHz and a waveguide characteristic impedance Z = 1000 Ω. c, Measured group delay of the high-Z waveguide. The coupled mechanical modes appear as sharp peaks in group delay.

Source data

Extended Data Fig. 2 Microwave-to-optical conversion with different microwave resonator frequencies.

Plot of normalized microwave-to-optical conversion S parameter as a function of frequency and coil current. The mechanical resonance frequencies do not shift with coil current and therefore appear as vertical lines. Soμ increases when a microwave mode is tuned into resonance with a mechanical mode.

Source data

Extended Data Fig. 3 Thermal occupation and heating.

a, Thermal phonon occupation of the mechanical mode versus repetition time of the optical pump pulse. As explained in Methods, the thermal occupation is calculated from sideband asymmetry between the blue- and red-detuned pump pulse. The error bars correspond to the standard deviation over 23 sets of sideband asymmetry measurements with data points representing the mean values. b, Time-domain heating of the optical pulse at 6 μs repetition, measured with microwave readout of the mechanical mode. Variance of the microwave noise is measured and calibrated to thermal phonon number with optical sideband asymmetry. Dashed red line is the exponential fit of the decaying tail of the thermal phonon occupation.

Source data

Extended Data Fig. 4 Optical setup.

Diagram representing the optical setup used in the experiment.

Extended Data Fig. 5 Demodulation efficiency and timing.

a, Calculated intracavity phonon and output photon flux versus time of the transducer with one initial phonon using coupled-mode theory. b, Calculated microwave measurement efficiency using different demodulation waveforms. Matched waveform gives the highest possible efficiency and is limited by device internal loss. c, Added noise in the microwave photon. The temporal heating is a theory fit to the time-domain heating measurement, assuming a bath with exponentially decaying thermal noise excited by the laser pulse. The temporal mode of the single photon is shown in comparison. The measured temporal heating is shown as grey dots. d, Measurement of the best demodulation timing for different demodulation waveforms. Efficiency of the demodulation is measured by the relative variance of post-selected state IQ data from single photon detection events versus the thermal state IQ, explained in detail in Methods. Black curves are control calculations using randomly selected IQ data instead of post-selected. Error bars are the standard deviation over 8 sets of measurements with data points being the mean values. e, Microwave Sμμ with no optical pump. 50 measurements, taken in quick succession of each other are plotted (blue) where one of them is highlighted for clarity (blue dots). The red curve shows the fit result from coupled-mode theory. For some traces the mechanical mode is undercoupled while for others it is overcoupled due to fluctuations of the intrinsic mechanical loss rate. The frequency is also stochastically jumping around. When the optical pump is turned on, the mechanical mode becomes more stable and its linewidth increases to ~ 1 MHz. These effects are possibly due to two-level systems (TLS).

Source data

Extended Data Fig. 6 Microwave setup.

Diagram representing the microwave setup used in the experiment. The dilution refigerator is highlighted in blue.

Extended Data Table 1 Device and system parameters
Full size table
Extended Data Table 2 Device and system efficiencies
Full size table

Supplementary information

Supplementary Information

Supplementary Figs. 1–3 and discussion.

Source data

Source Data Fig. 2

Transducer characterization data.

Source Data Fig. 3

Heralding data.

Source Data Extended Data Fig./Table 1

Microwave resonator characterization data.

Source Data Extended Data Fig./Table 2

Microwave-to-optical conversion vs coil current data.

Source Data Extended Data Fig./Table 3

Thermal occupation and heating data.

Source Data Extended Data Fig./Table 5

Demodulation efficiency and timing data.

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Jiang, W., Mayor, F.M., Malik, S. et al. Optically heralded microwave photon addition. Nat. Phys. 19, 1423–1428 (2023). https://doi.org/10.1038/s41567-023-02129-w

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