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A coherent spin–photon interface in silicon

Abstract

Electron spins in silicon quantum dots are attractive systems for quantum computing owing to their long coherence times and the promise of rapid scaling of the number of dots in a system using semiconductor fabrication techniques. Although nearest-neighbour exchange coupling of two spins has been demonstrated, the interaction of spins via microwave-frequency photons could enable long-distance spin–spin coupling and connections between arbitrary pairs of qubits (‘all-to-all’ connectivity) in a spin-based quantum processor. Realizing coherent spin–photon coupling is challenging because of the small magnetic-dipole moment of a single spin, which limits magnetic-dipole coupling rates to less than 1 kilohertz. Here we demonstrate strong coupling between a single spin in silicon and a single microwave-frequency photon, with spin–photon coupling rates of more than 10 megahertz. The mechanism that enables the coherent spin–photon interactions is based on spin–charge hybridization in the presence of a magnetic-field gradient. In addition to spin–photon coupling, we demonstrate coherent control and dispersive readout of a single spin. These results open up a direct path to entangling single spins using microwave-frequency photons.

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Figure 1: Spin–photon interface.
Figure 2: Strong single spin–photon coupling.
Figure 3: Electrical control of spin–photon coupling.
Figure 4: Quantum control and dispersive readout of a single spin.

References

  1. Tyryshkin, A. M. et al. Electron spin coherence exceeding seconds in high-purity silicon. Nat. Mater. 11, 143–147 (2012)

    Article  ADS  CAS  Google Scholar 

  2. Saeedi, K. et al. Room-temperature quantum bit storage exceeding 39 minutes using ionized donors in silicon-28. Science 342, 830–833 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  3. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)

    Article  ADS  CAS  Google Scholar 

  4. Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005)

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Neumann, P. et al. Multipartite entanglement among single spins in diamond. Science 320, 1326–1329 (2008)

    Article  ADS  CAS  PubMed  Google Scholar 

  6. Dehollain, J. P. et al. Bell’s inequality violation with spins in silicon. Nat. Nanotechnol. 11, 242–246 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  7. Zwanenburg, F. A. et al. Silicon quantum electronics. Rev. Mod. Phys. 85, 961–1019 (2013)

    Article  ADS  CAS  Google Scholar 

  8. Veldhorst, M. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nanotechnol. 9, 981–985 (2014)

    Article  ADS  CAS  PubMed  Google Scholar 

  9. Takeda, K. et al. A fault-tolerant addressable spin qubit in a natural silicon quantum dot. Sci. Adv. 2, e1600694 (2016)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  10. Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  11. Zajac, D. M. et al. Resonantly driven CNOT gate for electron spins. Science 359, 439–442 (2018)

    Article  ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  12. Watson, T. F. et al. A programmable two-qubit quantum processor in silicon. Nature https://doi.org/10.1038/nature25766 (2018)

  13. McNeil, R. P. G. et al. On-demand single-electron transfer between distant quantum dots. Nature 477, 439–442 (2011)

    Article  ADS  CAS  PubMed  Google Scholar 

  14. Baart, T. A. et al. Single-spin CCD. Nat. Nanotechnol. 11, 330–334 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  15. Bertrand, B. et al. Fast spin information transfer between distant quantum dots using individual electrons. Nat. Nanotechnol. 11, 672–676 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  16. Flentje, H. et al. Coherent long-distance displacement of individual electron spins. Nat. Commun. 8, 501 (2017)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  17. Baart, T. A., Fujita, T., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Coherent spin-exchange via a quantum mediator. Nat. Nanotechnol. 12, 26–30 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Bruhat, L. E . et al. Strong coupling between an electron in a quantum dot circuit and a photon in a cavity. Preprint at https://arxiv.org/abs/1612.05214 (2016)

  19. Mi, X., Cady, J. V., Zajac, D. M., Deelman, P. W. & Petta, J. R. Strong coupling of a single electron in silicon to a microwave photon. Science 355, 156–158 (2017)

    Article  ADS  CAS  PubMed  Google Scholar 

  20. Stockklauser, A. et al. Strong coupling cavity QED with gate-defined double quantum dots enabled by a high impedance resonator. Phys. Rev. X 7, 011030 (2017)

    Google Scholar 

  21. Thompson, R. J., Rempe, G. & Kimble, H. J. Observation of normal-mode splitting for an atom in an optical cavity. Phys. Rev. Lett. 68, 1132–1135 (1992)

    Article  ADS  CAS  PubMed  Google Scholar 

  22. Brune, M. et al. Quantum Rabi oscillation: a direct test of field quantization in a cavity. Phys. Rev. Lett. 76, 1800–1803 (1996)

    Article  ADS  CAS  PubMed  MATH  Google Scholar 

  23. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)

    Article  ADS  CAS  PubMed  Google Scholar 

  24. Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)

    Article  ADS  CAS  Google Scholar 

  25. Childress, L., Sorensen, A. S. & Lukin, M. D. Mesoscopic cavity quantum electrodynamics with quantum dots. Phys. Rev. A 69, 042302 (2004)

    Article  ADS  CAS  Google Scholar 

  26. Imamoğlu, A. Cavity QED based on collective magnetic dipole coupling: spin ensembles as hybrid two-level systems. Phys. Rev. Lett. 102, 083602 (2009)

    Article  ADS  CAS  PubMed  Google Scholar 

  27. Schuster, D. I. et al. High-cooperativity coupling of electron-spin ensembles to superconducting cavities. Phys. Rev. Lett. 105, 140501 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  28. Amsüss, R. et al. Cavity QED with magnetically coupled collective spin states. Phys. Rev. Lett. 107, 060502 (2011)

    Article  ADS  CAS  PubMed  Google Scholar 

  29. Bienfait, A. et al. Controlling spin relaxation with a cavity. Nature 531, 74–77 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  30. Eichler, C. et al. Electron spin resonance at the level of 104 spins using low impedance superconducting resonators. Phys. Rev. Lett. 118, 037701 (2017)

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Trif, M., Golovach, V. N. & Loss, D. Spin dynamics in InAs nanowire quantum dots coupled to a transmission line. Phys. Rev. B 77, 045434 (2008)

    Article  ADS  CAS  Google Scholar 

  32. Cottet, A. & Kontos, T. Spin quantum bit with ferromagnetic contacts for circuit QED. Phys. Rev. Lett. 105, 160502 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  33. Hu, X., Liu, Y.-x. & Nori, F. Strong coupling of a spin qubit to a superconducting stripline cavity. Phys. Rev. B 86, 035314 (2012)

    Article  ADS  CAS  Google Scholar 

  34. Beaudoin, F., Lachance-Quirion, D., Coish, W. A. & Pioro-Ladriere, M. Coupling a single electron spin to a microwave resonator: controlling transverse and longitudinal couplings. Nanotechnology 27, 464003 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  35. Frey, T. et al. Dipole coupling of a double quantum dot to a microwave resonator. Phys. Rev. Lett. 108, 046807 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  36. Petersson, K. D. et al. Circuit quantum electrodynamics with a spin qubit. Nature 490, 380–383 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  37. Viennot, J. J., Dartiailh, M. C., Cottet, A. & Kontos, T. Coherent coupling of a single spin to microwave cavity photons. Science 349, 408–411 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  38. Kawakami, E. et al. Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. Nat. Nanotechnol. 9, 666–670 (2014)

    Article  ADS  CAS  PubMed  Google Scholar 

  39. Burkard, G. & Imamoglu, A. Ultra-long-distance interaction between spin qubits. Phys. Rev. B 74, 041307 (2006)

    Article  ADS  CAS  Google Scholar 

  40. Jin, P.-Q., Marthaler, M., Shnirman, A. & Schon, G. Strong coupling of spin qubits to a transmission line resonator. Phys. Rev. Lett. 108, 190506 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  41. Benito, M., Mi, X., Taylor, J. M., Petta, J. R. & Burkard, G. Input-output theory for spin-photon coupling in Si double quantum dots. Phys. Rev. B 96, 235434 (2017)

    Article  ADS  Google Scholar 

  42. Schuster, D. I. et al. ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field. Phys. Rev. Lett. 94, 123602 (2005)

    Article  ADS  CAS  PubMed  Google Scholar 

  43. Mi, X. et al. Circuit quantum electrodynamics architecture for gate-defined quantum dots in silicon. Appl. Phys. Lett. 110, 043502 (2017)

    Article  ADS  CAS  Google Scholar 

  44. Mi, X., Peterfalvi, C. G., Burkard, G. & Petta, J. R. High-resolution valley spectroscopy of Si quantum dots. Phys. Rev. Lett. 119, 176803 (2017)

    Article  ADS  CAS  PubMed  Google Scholar 

  45. Probst, S. et al. Inductive-detection electron-spin resonance spectroscopy with 65 spins/√Hz sensitivity. Appl. Phys. Lett. 111, 202604 (2017)

    Article  ADS  CAS  Google Scholar 

  46. Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  47. Sillanpää, M. A., Park, J. I. & Simmonds, R. W. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438–442 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  48. Zajac, D. M., Hazard, T. M., Mi, X., Wang, K. & Petta, J. R. A reconfigurable gate architecture for Si/SiGe quantum dots. Appl. Phys. Lett. 106, 223507 (2015)

    Article  ADS  CAS  Google Scholar 

  49. Elzerman, J. M. et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004)

    Article  ADS  CAS  PubMed  Google Scholar 

  50. Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)

    Article  ADS  CAS  Google Scholar 

  51. Debnath, S. et al. Demonstration of a small programmable quantum computer with atomic qubits. Nature 536, 63–66 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  52. Nigg, S. E ., Fuhrer, A . & Loss, D. Superconducting grid-bus surface code architecture for hole-spin qubits. Phys. Rev. Lett. 118, 147701 (2017)

    Article  ADS  PubMed  Google Scholar 

  53. Samkharadze, N . et al. Strong spin-photon coupling in silicon. Preprint at https://arxiv.org/abs/1711.02040 (2017)

  54. Landig, A. J . et al. Coherent spin-qubit photon coupling. Preprint at https://arxiv.org/abs/1711.01932 (2017)

  55. Wallraff, A. et al. Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005)

    Article  ADS  CAS  PubMed  Google Scholar 

  56. Wallraff, A., Stockklauser, A., Ihn, T., Petta, J. R. & Blais, A. Comment on “Vacuum Rabi splitting in a semiconductor circuit QED system”. Phys. Rev. Lett. 111, 249701 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  57. Rau, I., Johansson, G. & Shnirman, A. Cavity quantum electrodynamics in superconducting circuits: Susceptibility at elevated temperatures. Phys. Rev. B 70, 054521 (2004)

    Article  ADS  CAS  Google Scholar 

  58. Yoneda, J . et al. A >99:9% fidelity quantum-dot spin qubit with coherence limited by charge noise. Preprint at https://arxiv.org/abs/1708.01454 (2017)

  59. Samkharadze, N. et al. High-kinetic-inductance superconducting nanowire resonators for circuit QED in a magnetic field. Phys. Rev. Appl. 5, 044004 (2016)

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

We thank A. J. Sigillito for technical assistance and M. J. Gullans for discussions. This work was supported by the US Department of Defense under contract H98230-15-C0453, Army Research Office grant W911NF-15-1-0149, and the Gordon and Betty Moore Foundations EPiQS Initiative through grant GBMF4535. Devices were fabricated in the Princeton University Quantum Device Nanofabrication Laboratory.

Author information

Authors and Affiliations

Authors

Contributions

X.M. fabricated the sample and performed the measurements. X.M., D.M.Z. and J.R.P. developed the design and fabrication process for the DQD. X.M. and S.P. developed the niobium cavity fabrication process. M.B., G.B., J.M.T. and J.R.P. developed the theory for the experiment. X.M., M.B. and J.M.T. analysed the data. X.M., J.R.P., G.B. and J.M.T. wrote the manuscript with input from the other authors. J.R.P. planned and supervised the experiment.

Corresponding author

Correspondence to J. R. Petta.

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Competing interests

X.M., J.R.P., D.M.Z. and Princeton University have filed a provisional US patent application related to spin–photon transduction.

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Reviewer Information Nature thanks T. Meunier and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Figure 1 Micromagnet design.

To-scale drawing of the micromagnet design, superimposed on top of the SEM image of the DQD. The coordinate axes and the direction of the externally applied magnetic field are indicated at the bottom. In this geometry, the DQD electron experiences a homogeneous z field . The total x field Bx that is experienced by the electron is spatially dependent, being approximately () when the electron is in the L (R) dot () and when the electron is delocalized between the DQDs (ε = 0). The y field By for the DQD electron is expected to be small compared to the other field components for this magnet design.

Extended Data Figure 2 Photon number calibration.

The ESR resonance frequency fESR, measured using the phase response of the cavity Δϕ in the dispersive regime (Fig. 4b), is plotted as a function of the estimated power at the input port of the cavity P (data). The device is configured with gs/(2π) = 2.4 MHz and spin–photon detuning Δ/(2π) ≈ −18 MHz. The dashed line shows a fit to , where nph is the average number of photons in the cavity, plotted as the top x axis. The experiments are conducted with P ≈ −133 dBm (0.05 fW), which corresponds to nph ≈ 0.6. The error bars indicate the uncertainties in the centre frequency of the ESR transition.

Source data

Extended Data Figure 3 DQD stability diagrams.

The cavity transmission amplitude A/A0 (a, c) and phase response Δϕ (b, d) are plotted as functions of VP1 and VP2 for DQD1 (a, b) and DQD2 (c, d), obtained with f = fc. The (1, 0) ↔ (0, 1) transitions are clearly identified on the basis of these measurements and subsequently tuned close to resonance with the cavity for the experiments described in the main text. The red circles indicate the locations of the (1, 0) ↔ (0, 1) transitions of the two DQDs.

Source data

Extended Data Figure 4 Spin decoherence rates at different DQD tunnel couplings.

ESR line, as measured in the cavity phase response Δϕ(fs), is shown for different values of 2tc/h in the low-power limit (data). ε = 0 for every dataset. Dashed lines are fits with Lorentzian functions and γs/(2π) is determined as the half-width at half-maximum of each Lorentzian. The spin–photon detuning |Δ|≈10 gs for each dataset, to ensure that the system is in the dispersive regime.

Source data

Extended Data Figure 5 Spin–photon coupling strengths at different DQD tunnel couplings.

a, b, Vacuum Rabi splittings for 2tc/h < fc (a) and 2tc/h > fc (b), obtained by varying until a pair of resonance peaks with approximately equal heights emerges in the cavity transmission spectrum A/A0. gs/(2π) is then estimated as half the frequency difference between the two peaks. ε = 0 for every dataset. gs is difficult to measure for 5.2 GHz < 2tc/h < 6.7 GHz owing to the small values of A/A0 that arise from the large spin decoherence rates γs in this regime.

Source data

Extended Data Figure 6 Spin relaxation at ε = 0.

The time-averaged phase response of the cavity Δϕ is shown as a function of wait time TM (data), measured using the pulse sequence illustrated in Fig. 4c. The microwave burst time is fixed at τB = 80 ns. The dashed line shows a fit using the function ϕ0 + ϕ1(T1/TM)[1 − exp(−TM/T1)], which yields a spin relaxation time of T1 ≈ 3.2 μs. The experimental conditions are the same as for Fig. 4d.

Source data

Extended Data Figure 7 Theoretical fits to vacuum Rabi splittings.

The calculated cavity transmission spectra (black solid lines) are superimposed on the experimentally measured vacuum Rabi splittings shown in Fig. 2b, c (data). The calculations are produced with gc/(2π) = 40 MHz (gc/(2π) = 37 MHz), κ/(2π) = 1.8 MHz, γc/(2π) = 105 MHz (γc/(2π) = 120 MHz), , and 2tc/h = 7.4 GHz for DQD1 (DQD2). For comparison, A(f)/A0, simulated for a two-level charge qubit with a decoherence rate of γc/(2π) = 2.4 MHz coupled to a cavity with κ/(2π) = 1.8 MHz at a rate gc/(2π) = 5.5 MHz, is shown in a for thermal photon numbers of nth = 0.02 (black dashed line) and nth = 0.5 (red dashed line).

Source data

Extended Data Figure 8 Prospect for long-range spin–spin coupling.

a, The ratio 2gs/(κ/2 + γs) as a function of 2tc/h, calculated using the data in Fig. 3b and κ/(2π) = 1.8 MHz. b, The ratio gs/γs as a function of 2tc/h, also calculated using the data in Fig. 3b.

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Mi, X., Benito, M., Putz, S. et al. A coherent spin–photon interface in silicon. Nature 555, 599–603 (2018). https://doi.org/10.1038/nature25769

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