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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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.
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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.
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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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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.
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.
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.
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.
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.
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).
Extended Data Figure 8 Prospect for long-range spin–spin coupling.
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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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DOI: https://doi.org/10.1038/nature25769
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