Research ArticleCONDENSED MATTER PHYSICS

Electrically controlling single-spin qubits in a continuous microwave field

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Science Advances  10 Apr 2015:
Vol. 1, no. 3, e1500022
DOI: 10.1126/sciadv.1500022
  • Fig. 1 Electric field dependence of electron and nuclear energy states.

    (A) False-colored scanning electron microscope image of a device similar to the one used in the experiment. Blue, microwave (MW) antenna; yellow, gates used to induce the SET charge sensor under the SiO2 insulator; pink, A-gates, comprising gates labeled Donor Fast (DF), Donor Slow (DS), and Top Gate AC (TGAC). These gates are used to tune the potential and electric field at the donor location. (B) Electron wavefunction of a donor under an electrostatic gate. A positive voltage applied to the gate attracts the electron toward the Si-SiO2 interface. For illustration purposes, the wavefunction distortion is largely exaggerated as compared to the actual effect taking place in the experiment. (C) Energy level diagram of the neutral e-31P system. Gate-controlled distortion of the electron wavefunction modifies A and γe, shifting the ESR νe1 and νe2, and the NMR νn1 and νn2 transition frequencies.

  • Fig. 2 Local electrical control of the ESR transition frequencies.

    (A) Schematic of the charge stability diagram for this device. The thick solid lines represent the Coulomb peaks of the SET, whereas the dashed line indicates the ionization/neutralization of the donor. (B) Measured shift in ESR frequencies νe1,2(VA) as a function of the A-gate voltage VA. Accurate values of νe1,2(VA) are obtained by coherent Ramsey experiments (see text). The change in local electric field is obtained from finite element electrostatic modeling for the specific device geometry and donor location (see section S6 for details).

  • Fig. 3 Electrically controlled qubit control and coherence measurements.

    (A) Schematic of the sequence used to measure EC Rabi oscillations. (B and C) EC Rabi oscillations measured on the 31P electron and nucleus, respectively. (D) Schematic of the sequence used to measure EC Ramsey oscillations. (E and F) EC Ramsey oscillations measured on the 31P electron and nucleus. (G) Schematic of the sequence used to measure EC coherence times. (H and I) EC Hahn echo decay for the 31P electron and nucleus. (J and K) Extended spin coherence times T2 for CPMG dynamical decoupling sequences on the 31P electron and nucleus.

  • Fig. 4 Electrically controlled gate fidelities.

    (A and B) EC randomized benchmarking performed on the 31P electron and nucleus, respectively. Shaded circles are the results of individual measurements (that is, individual random sequences of gate operations), whereas the solid circles show the average state survival probability of all random sequences with the same number of gate operations.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/3/e1500022/DC1

    Fig. S1. Frequency response.

    Fig. S2. Donor triangulation.

    Fig. S3. Electric field simulations.

    Fig. S4. Electric field simulations.

    Fig. S5. Electric field simulations.

    Fig. S6. Atomistic tight binding simulations of the hyperfine coupling for a donor at the location determined in section S5, for the electric fields simulated in section S6, and subject to lattice strain.

    Fig. S7. Electrically controlled ESR spectrum.

    Fig. S8. Time evolution simulations of the electrically controlled ESR spectrum.

    Fig. S9. Electrically controlled Rabi spectrum.

    Fig. S10. Electrically controlled electron Ramseys.

    Fig. S11. Electrically controlled nuclear Ramseys.

    Fig. S12. Electrically controlled electron coherence times.

    Fig. S13. Electrically controlled nuclear coherence times.

    Table S1. Relative gate capacitances used for triangulation of the donor position.

    References (3554)

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Frequency response.
    • Fig. S2. Donor triangulation.
    • Fig. S3. Electric field simulations.
    • Fig. S4. Electric field simulations.
    • Fig. S5. Electric field simulations.
    • Fig. S6. Atomistic tight binding simulations of the hyperfine coupling for a donor at the location determined in section S5, for the electric fields simulated in section S6, and subject to lattice strain.
    • Fig. S7. Electrically controlled ESR spectrum.
    • Fig. S8. Time evolution simulations of the electrically controlled ESR spectrum.
    • Fig. S9. Electrically controlled Rabi spectrum.
    • Fig. S10. Electrically controlled electron Ramseys.
    • Fig. S11. Electrically controlled nuclear Ramseys.
    • Fig. S12. Electrically controlled electron coherence times.
    • Fig. S13. Electrically controlled nuclear coherence times.
    • Table S1. Relative gate capacitances used for triangulation of the donor position.
    • References (35–54)

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