Role of metastable charge states in a quantum-dot spin-qubit readout

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Role of metastable charge states in a quantum-dot spin-qubit readout

J. D. Mason, S. A. Studenikin, A. Kam, Z. R. Wasilewski, A. S. Sachrajda, and J. B. Kycia

Phys. Rev. B 92, 125434 – Published 25 September 2015

Abstract

Readout of a spin qubit in a lateral gate-defined quantum-dot device typically involves a charge detector and a spin-to-charge conversion technique employing spin blockade. We investigate alternative mechanisms for spin-to-charge conversion involving metastable excited charge states made possible by an asymmetry in the tunneling rates to the leads. This technique is used to observe Landau-Zener-Stückelberg oscillations of the $S - T_{+}$ qubit within the (1,0) ground state region of the charge stability diagram. The oscillations are $π$ phase shifted relative to those detected using the standard technique and display a nonsinusoidal waveform due to the increased relaxation time from the metastable state.

Received 8 July 2015
Revised 3 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.125434

Authors & Affiliations

J. D. Mason¹, S. A. Studenikin², A. Kam², Z. R. Wasilewski^2,*, A. S. Sachrajda², and J. B. Kycia^1,†

¹Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
²National Research Council Canada, Ottawa, ON K1A 0R6, Canada

^*Present address: Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada.
^†Corresponding author: jkycia@uwaterloo.ca

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Vol. 92, Iss. 12 — 15 September 2015

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Images

Figure 1
(a) Gray scale plot of the transconductance of the QPC charge detector in the few electron regime of the DQD. The diagram is divided into charge stable regions labeled ( $N_{L}, N_{R}$ ). Charging lines (black) and extensions of charging lines (yellow dash) form boundaries between the regions labeled R1, R2, R3, and R4. Inset: Scanning electron micrograph of the DQD gate layout. The high bandwidth gates are labeled 1 and 2. The QPC used in the transconductance measurements is indicated with an arrow labeled $I_{QPC}$ . The 80 mT magnetic field is applied in the direction of the arrow labeled $B$ . (b) Energy level diagram of the two-electron spin states showing the avoided crossing involving the S and $T_{+}$ qubit states [dash-dot in (a)]. Below this diagram is shown a Gaussian pulse. Such pulses are applied to gates 1 and 2 to produce the trajectory represented by the arrow connecting points M and P in (a).
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Figure 2
Stability diagram of the DQD acquired in the presence of a gate pulse (lock-in amplifier time constant 1 s). The pulse has a width of 17 ns, a rise time of 8 ns, and a period of 2 $μ s$ . The black short-dashed line indicates the position of the missing charging line separating the (1,0) and (2,0) ground state regions. This line together with the extensions of charging lines (yellow long-dash) divide the diagram into regions labeled R1, R2, R3, and R4 as in Fig. 1. Spin state readout is accomplished using a metastable charge state in regions R2 and R3. The position of the (2,0) $\leftrightarrow$ (1,1) charge transfer line is indicated with a black dotted line. The lines labeled $ɛ_{1}, ɛ_{2}$ , and $ɛ_{3}$ indicate the positions of the line scans relevant to Fig. 5.
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Figure 3
The LZS oscillations in regions R1, R2, and R3 are outlined (yellow) in (a), (b), and (c) respectively. Arrows indicate examples of pulse trajectories. The (1,0) $\leftrightarrow$ (2,0) charging line and the (2,0) $\leftrightarrow$ (1,1) charge transfer line are shown as dashed and dotted lines, respectively. The position of the S- $T_{+}$ avoided crossing is indicated with a dash-dotted line. (d) Regions of telegraph noise resulting from fluctuations between the (1,0) and (2,0) charge states are outlined in yellow (boundaries A–D) and blue ( $*$ ).
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Figure 4
Schematic energy diagram for each of the four regions R1–R4 shown in Fig. 2. The processes by which each of the qubit states, S(1,1) and $T_{+}$ (1,1), eventually transitions to the ground state are also shown (metastable states in bold). The mechanism of spin-to-charge conversion in each region relies on mapping one of the qubit spin states to an excited charge state that is long-lived relative to the readout measurement time, $T_{m}$ . (a) Region R1: Standard readout of the S- $T_{+}$ qubit. The S(1,1) state transitions to the S(2,0) singlet ground state while $T_{+}$ (1,1) remains in the (1,1) excited charge state for a time $T_{1}$ due to spin blockade. (b) Region R2: Metastable excited state used in the readout. Due to the strong coupling of the right dot to its lead, an electron is rapidly ejected from the right dot and $T_{+}$ (1,1) transitions to the (1,0) charge state. This excited state is metastable due to the slow tunnel rate between the left dot and the leads, $T_{L}$ . (c) Region R3: Metastable excited state and single electron ground state used in the readout. The $T_{+}$ (1,1) state transitions to the (1,0) ground state due to the strong coupling of the right dot to its lead and S(1,1) transitions to the S(2,0) metastable excited state. (d) Region R4: The (2,1) first excited state is not metastable for our choice of lead couplings and as a result plays no role in the spin-to-charge conversion mechanism.
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Figure 5
Plots of transconductance as a function of initial detuning along $V_{1}$ and pulse duration for regions R1 (a), R2 (c), and R3 (e) (lock-in amplifier time constant 300 ms). The vertical axes correspond to projections onto the $V_{1}$ axis of the trajectories shown as black lines labeled $ɛ_{1}, ɛ_{2}$ , and $ɛ_{3}$ in Fig. 2 (differences between the vertical axis gate voltages and those expected from Fig. 2 are due to device drift). (b), (d), and (f) Line scans through the data of (a), (c), and (e) taken at the positions of the vertical dashed lines.
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