Research ArticleCONDENSED MATTER PHYSICS

Readout and control of the spin-orbit states of two coupled acceptor atoms in a silicon transistor

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Science Advances  07 Dec 2018:
Vol. 4, no. 12, eaat9199
DOI: 10.1126/sciadv.aat9199
  • Fig. 1 Detection of a single acceptor atom.

    (A) Scanning electron microscopy image of the used tri-gate transistor in a schematic diagram of the experimental setup for transport and RF gate reflectometry measurements. The magnetic field in this experiment is applied along the y direction (along the channel). (B) Change in reflected phase from the LC circuit (red) compared to the measured source-drain current (blue), both at 1 mV VD. The signals of a boron atom (black arrow) and an unintentional quantum dot (gray arrows) are identified. BOX, buried oxide.

  • Fig. 2 Two-hole system.

    (A) Reflected amplitude and phase response showing a break in the acceptor-lead charging line (red) caused by the charging of a nearby acceptor atom (dashed lines). (B and C) Measured and calculated magnetic field dependence of the interacceptor tunneling phase response. The magnetic fields yielding the singlet-triplet crossing BST and singlet-quadruplet crossing BSQ are plotted in (C) as a function of detuning by dashed curves. (D) Schematic overview of the relevant two-hole states. The (1,1) and (2,0) SHH states (blue), (1,1) THH states (green), and (2,0) QLH states (red) are shown. While this subset of two-hole states is sufficient to describe our experiments, a full description of the spin-orbit states can be found in section S3. Insets show a depiction of the potential landscape and possible spins involved in these states.

  • Fig. 3 Spin relaxation mechanisms of the two-hole system.

    (A) Time-averaged RF reflectometry amplitude (red) and phase (blue) measurement with continuous pulses applied to the drain, at a magnetic field of 1.5 T. The interacceptor tunneling is displaced from the break of the acceptor-lead tunneling signal by the Zeeman energy of the T ground state. (B) Relaxation time extracted from the time-dependent phase signal for a pulse between the points ε0 and ε1. (C) Magnetic field dependence of the relaxation rate T1−1. (D) Schematic view of the relevant relaxation rates in this system at the zero detuning point (see inset). The data in (C) are fit to a combination of the ΓS/QT rate (green line) and ΓST rate (blue line), resulting in the black line. This is compared to a fit using the ΓSQ rate (red line) instead of the ΓST rate.

  • Fig. 4 Excited states of the two-hole system measured by transport spectroscopy.

    (A) Transconductance dI/dVTG as a function of the top and back gate voltages at 10 mV VD. The bias triangle, marked by solid black lines, shows three excited states in addition to the ground state as indicated by arrows. (B) Level configuration of the A+ state, corresponding to the found excited states. (C) Magnetic field dependence of the transconductance at a cut through the bias triangle at 1.4 V VBG, as indicated by the dotted line in (A). At the bottom, arrows indicate the excited state spectrum as also shown in (A). Two changes in the slope of the ground state at 0.25 and 0.5 T are the result of the BST and BSQ crossings. (D) Model of the transition energies in the high–magnetic field limit. Top: Overview of the (1,1)→(2,0) transitions at a magnetic field of 1.3 T. Bottom: Simulated magnetic field behavior of the transition energy spectrum, using the g factors and ΔLH extracted from the transition energies in (C) and using the same line broadening as found in this experiment.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/12/eaat9199/DC1

    Section S1. Estimation of tunnel rates

    Section S2. Acceptor-based single-atom qubits

    Section S3. Two-hole states

    Section S4. Relaxation mechanisms

    Section S5. (1,1)→(2,0) transition energies

    Fig. S1. Transport spectroscopy images.

    Fig. S2. Frequency domain analysis of the reflectometry signal.

    Fig. S3. Interacceptor continuous-wave microwave excitation experiment.

    Fig. S4. Examples of the Zeeman effect on A0 states.

    Fig. S5. Examples of the Zeeman effect on two-hole states.

    Fig. S6. Relaxation rate models.

    References (4751)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Estimation of tunnel rates
    • Section S2. Acceptor-based single-atom qubits
    • Section S3. Two-hole states
    • Section S4. Relaxation mechanisms
    • Section S5. (1,1)→(2,0) transition energies
    • Fig. S1. Transport spectroscopy images.
    • Fig. S2. Frequency domain analysis of the reflectometry signal.
    • Fig. S3. Interacceptor continuous-wave microwave excitation experiment.
    • Fig. S4. Examples of the Zeeman effect on A0 states.
    • Fig. S5. Examples of the Zeeman effect on two-hole states.
    • Fig. S6. Relaxation rate models.
    • References (4751)

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