Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200μs

Journal name:
Nature Physics
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Qubits, the quantum mechanical bits required for quantum computing, must retain their quantum states for times long enough to allow the information contained in them to be processed. In many types of electron-spin qubits, the primary source of information loss is decoherence due to the interaction with nuclear spins of the host lattice. For electrons in gate-defined GaAs quantum dots, spin-echo measurements have revealed coherence times of about 1μs at magnetic fields below 100mT (refs 1, 2). Here, we show that coherence in such devices can survive much longer, and provide a detailed understanding of the measured nuclear-spin-induced decoherence. At fields above a few hundred millitesla, the coherence time measured using a single-pulse spin echo is 30μs. At lower fields, the echo first collapses, but then revives at times determined by the relative Larmor precession of different nuclear species. This behaviour was recently predicted3, 4, and can, as we show, be quantitatively accounted for by a semiclassical model for the dynamics of electron and nuclear spins. Using a multiple-pulse Carr–Purcell–Meiboom–Gillecho sequence, the decoherence time can be extended to more than 200μs, an improvement by two orders of magnitude compared with previous measurements1, 2, 5.

At a glance


  1. Qubit control.
    Figure 1: Qubit control.

    a, Scanning electron micrograph of a device similar to the one used. Metal gates (bright structures) are negatively biased to confine two electrons. The charge state of the double quantum dot is determined by measuring the conductance through the capacitively coupled QPC, GQPC. The separation between the two electrons is controlled with nanosecond time resolution using the voltages on GR and GL. b, Left: An initially prepared singlet state oscillates between S and T0 with frequency g*μBΔBnucz/planck, which changes over time as a result of slow fluctuations of the hyperfine field gradient ΔBnucz. Right: Switching on the tunnel coupling between the two dots leads to the coherent exchange of the electron spins. c, Hahn-echo sequence. After evolving for a time τ/2, the two electrons are exchanged with a π-pulse. The singlet state is recovered after further evolution for another τ/2, independent of ΔBnucz. d, CPMG sequence. In this higher-order decoupling sequence, nπ-pulses at time intervals τ/n are applied.

  2. Echo amplitude.
    Figure 2: Echo amplitude.

    a, Echo signal as a function of the total evolution time, τ, for different values of magnetic field. The fits to the data are obtained by extending the model of ref. 3 to include a spread δBloc of the nuclear Larmor frequencies and multiplying by exp((−τ/TSD)4). Curves are offset for clarity and normalized as discussed in the Supplementary Information. b, The total Zeeman field seen by the electron is the vector sum of the external field and the Overhauser fields parallel and perpendicular to it. c, The three nuclear species (only two shown for clarity) contributing to the Overhauser field precession at different Larmor frequencies in the external field. d, As a result of the relative precession, the total transverse nuclear field oscillates at the Larmor frequency difference(s).

  3. CPMG decoupling experiments with 6, 10 and 16 [pi]-pulses at Bext=0.4[thinsp]T.
    Figure 3: CPMG decoupling experiments with 6, 10 and 16 π-pulses at Bext=0.4T.

    The blue dots show the readout signal of the CPMG pulses; the red circles represent reference measurements with the same evolution time without any π-pulses (equivalent to T2* measurements), which produce a completely dephased state. PS is the sensor signal normalized by the d.c. contrast associated with the transfer of an electron from one dot to the other, so that a singlet corresponds to PS=1 (see Supplementary Information). Inelastic decay during the readout phase and possibly other visibility loss mechanisms increase PS compared with the actual singlet probability p(S), so that the value for the mixed state exceeds the ideal value of 0.5. The linear trends in the reference and the initial decay of the CPMG signal possibly reflect leakage out of the logical subspace. The linear fits to the 16-pulse data (black lines) intersect at τ=276μs, which can be taken as a rough estimate or lower bound of the coherence time.


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Author information

  1. These authors contributed equally to this work

    • Hendrik Bluhm &
    • Sandra Foletti


  1. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    • Hendrik Bluhm,
    • Sandra Foletti,
    • Izhar Neder,
    • Mark Rudner &
    • Amir Yacoby
  2. Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

    • Diana Mahalu &
    • Vladimir Umansky


Electron-beam lithography and molecular-beam-epitaxy growth were carried out by D.M. and V.U., respectively. H.B., S.F. and A.Y. fabricated the sample, planned and executed the experiment and analysed the data. I.N., M.R., H.B. and A.Y. developed the theoretical model. H.B., S.F., I.N., M.R. and A.Y. wrote the paper.

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