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Ideal refocusing of an optically active spin qubit under strong hyperfine interactions

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Abstract

Combining highly coherent spin control with efficient light-matter coupling offers great opportunities for quantum communication and computing. Optically active semiconductor quantum dots have unparalleled photonic properties but also modest spin coherence limited by their resident nuclei. The nuclear inhomogeneity has thus far bound all dynamical decoupling measurements to a few microseconds. Here, we eliminate this inhomogeneity using lattice-matched GaAs–AlGaAs quantum dot devices and demonstrate dynamical decoupling of the electron spin qubit beyond 0.113(3) ms. Leveraging the 99.30(5)% visibility of our optical π-pulse gates, we use up to Nπ = 81 decoupling pulses and find a coherence time scaling of \({N}_{\uppi }^{0.75(2)}\). This scaling manifests an ideal refocusing of strong interactions between the electron and the nuclear spin ensemble, free of extrinsic noise, which holds the promise of lifetime-limited spin coherence. Our findings demonstrate that the most punishing material science challenge for such quantum dot devices has a remedy and constitute the basis for highly coherent spin–photon interfaces.

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Fig. 1: Optically addressable spin in a GaAs–AlGaAs QD.
Fig. 2: Complete qubit control.
Fig. 3: Electron spin coherence.
Fig. 4: Key parameters for device performance.

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Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

Code availability

The code that models the decoherence of the dynamically decoupled electron spin is available at https://github.com/CoherentQD/CPMG_simulation.

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Acknowledgements

We acknowledge support from the Royal Society (EA/181068; C.L.G.), the US Office of Naval Research Global (N62909-19-1-2115; M.A.), the EU Horizon 2020 FET Open project QLUSTER (862035; C.L.G. and M.A.), the EU Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant QUDOT-TECH (861097; M.A.), Qurope (899814; A.R.), ASCENT+ (871130; A. R.), Engineering and Physical Sciences Research Council grant EP/V048333/1 (E.A.C.) and the Austrian Science Fund (FWF; FG 5, P 30459, I 4380, I 4320 and I 3762; A.R.), the LIT Secure and Correct Systems Lab platform is funded by the state of Upper Austria. L.Z., J.H.B. and D.M.J. acknowledge support from the EPSRC DTP. D.A.G. acknowledges a St. John’s College Fellowship and a Royal Society University Research Fellowship; C.LG., a Dorothy Hodgkin Royal Society Fellowship; and E.A.C., a Royal Society University Research Fellowship. We also thank Ł. Cywiński, M. E. Flatté, C. E. Pryor, H. Bluhm, P. Atkinson, A. J. Garcia, G. Undeutsch and P. Klenovský for fruitful discussions.

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Contributions

L.Z., D.A.G., M.A. and C.L.G. conceived the spin control experiments; E.A.C. conceived the NMR experiments; and E.A.C. and A.R. conceived the QD device. L.Z., J.H.B., N.S., M.H.A., G.D., G.P. and C.L.G. carried out the spin control and resonance fluorescence experiments; L.Z. and C.L.G. performed the corresponding data analysis, theory and simulations; G.G. and E.A.C. carried out the NMR experiments; S.M. and S.C.d.S. performed the molecular beam epitaxy growth; and C.S. characterized the samples. S.M., J.J. and N.S. processed the QD devices. All authors contributed to the discussion of the analysis and the results. All authors participated in the preparation of the manuscript.

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Correspondence to Leon Zaporski, Mete Atatüre or Claire Le Gall.

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Extended data

Extended Data Fig. 1 QD device.

Schematics of the QD device outlining the composition of the nip heterostructure (Linz Ref. SA0553), the electrical contacts (Methods) and the solid immersion lens (SIL).

Extended Data Fig. 2 Experimental set-up.

AOM = acousto-optic modulator; EOM = electro-optic modulator; APD = avalanche photodiode; AWG = arbitrary waveform generator. Colors of the laser beams correspond to the driven processes (readout, depolarization and spin control) outlined in the energy level diagram on the right.

Extended Data Fig. 3 π-pulse visibility.

a, Visibility measurement on a 40s timescale with Nπ = 162. The left panel displays the readout signal for \(\left\vert \uparrow \right\rangle\) -state initialization. The integrated counts under the yellow dark-shaded area are background-subtracted with the counts in the yellow light-shaded area, yielding cts = 1753. The right panel displays the readout signal following the same pulse sequence with an additional π-pulse (\(\left\vert \downarrow \right\rangle\)-state initialization) yielding cts = 917. This corresponds to a π-pulse visibility of \({{{\mathcal{F}}}}=99.30(5) \%\) (Methods). b, Visibility on long timescales. Data points display the fitted maximal visibility, \({v}_{\max }\), in long CPMG measurements as a function of the number of π-pulses in the sequence, Nπ. The black curve illustrates that a π-pulse visibility \(\bar{{{{\mathcal{F}}}}}=97.81(5) \%\) is typically achieved over longer integration times (Methods). The error bars represent the standard deviation errors on fit parameter \({v}_{\max }\).

Extended Data Fig. 4 NMR datasets.

a, Inverse NMR spectrum of nuclear transition frequencies resolved in an extrinsically strained device (\({\nu }_{Q}^{{{{\rm{ext}}}}}=250\) kHz), displaying a sharp central transition (CT) together with broader satellite transitions (ST). b, Inverse NMR lineshape of the blue-detuned satellite transition together with a skew-normal fit (the red solid curve), given by a function S(A)(ν) from Eq. (8) in Methods, with fitted parameters A = 158(1) μeV × kHz, μ(A) = 252.21(4) kHz, σ(A) = 9.74(8) kHz, ζ(A) = 3.22(8) and C = 0.72(3) μeV, corresponding to a FWHM = 22.9(2) kHz. c, Integral NMR spectrum of the blue-detuned satellite transition. The solid red curve displays the normalized cumulative distribution obtained from the fit to the data in Extended Data Fig. 4b (cf. Eq. (10) in Methods); the mismatch indicates the presence of a broader pedestal (see Fig. 4a), which we fit with a Gaussian distribution centred at μ(B) = 246(2) kHz with FWHM = 172(9) kHz and relative weight β = 0.244(7). The resulting sum fit, given by function CDF(ν) from Eq. (11) in Methods (normalized to 13.09 μeV), is displayed as the turquoise solid curve.

Extended Data Fig. 5 Global fit to the CPMG dataset.

The electronic coherence function from the Eq. (15), that is W(t), was calculated with our model and globally fitted to the CPMG data sub-sets (the black points) with: a, Nπ = 1, b, Nπ = 2, c, Nπ = 3, d, Nπ = 4, e, Nπ = 5, f, Nπ = 8, g, Nπ = 9, h, Nπ = 27 and i, Nπ = 81, all taken at B = 6.5 T. The set of the solid red curves displays the best global fit.

Extended Data Fig. 6 Assessing the goodness of the global fit to the CPMG dataset.

Weighted residual sum of squares per data point, averaged over all the CPMG data subsets of varied Nπ, as a function of two global fit parameters: β and scaling factor κ. Best global fit is found for β = 0.35 and κ = 1.45.

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Supplementary Figs. 1–3, Tables 1 and 2 and Discussion.

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Zaporski, L., Shofer, N., Bodey, J.H. et al. Ideal refocusing of an optically active spin qubit under strong hyperfine interactions. Nat. Nanotechnol. 18, 257–263 (2023). https://doi.org/10.1038/s41565-022-01282-2

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