Resonantly Driven Singlet-Triplet Spin Qubit in Silicon

K. Takeda, A. Noiri, J. Yoneda, T. Nakajima, and S. Tarucha

Phys. Rev. Lett. 124, 117701 – Published 20 March 2020

Abstract

We report implementation of a resonantly driven singlet-triplet spin qubit in silicon. The qubit is defined by the two-electron antiparallel spin states and universal quantum control is provided through a resonant drive of the exchange interaction at the qubit frequency. The qubit exhibits long $T_{2}^{*}$ exceeding $1 μ s$ that is limited by dephasing due to the ${}^{29}{Si}$ nuclei rather than charge noise thanks to the symmetric operation and a large micromagnet Zeeman field gradient. The randomized benchmarking shows 99.6% single gate fidelity which is the highest reported for singlet-triplet qubits.

Received 13 September 2019
Revised 12 December 2019
Accepted 20 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.117701

Physics Subject Headings (PhySH)

Quantum transport

Double quantum dots Quantum dots

Dilution refrigerator Electron spin resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

K. Takeda , A. Noiri , J. Yoneda ^*, T. Nakajima , and S. Tarucha

Center for Emergent Matter Science (CEMS), RIKEN, Wako-shi, Saitama 351-0198, Japan

^*Present address: School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales 2052, Australia.

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Vol. 124, Iss. 11 — 20 March 2020

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Images

Figure 1
(a) False colored scanning electron microscope image of the device. Three layers of overlapping aluminium gates are used to control the confinement potential. The screening gates (blue) are used to restrict the electric field of the plunger (red) and barrier (green) gates. (b) Schematic of device geometry and measurement setup. The device geometry shows a line cut along the white dashed line in Fig. 1. Three gates labeled as $P 1$ , $P 2$ , and $B 2$ are mainly used to control the DQD confinement. (c) Energy diagram of two-electron unpolarized spin states. (d) Charge stability diagram measured as a function of gate voltages $V_{P 1}$ and $V_{P 2}$ . The variation of the background signal is caused by the Coulomb oscillation of the radio-frequency sensor QD. The tick of the detuning axis indicates $ϵ = 0$ .
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Figure 2
(a) Measurement sequence of the resonantly driven spin qubit. $S_{L}$ and $S_{R}$ refers to the left and right spin, respectively. (b) Rabi chevron pattern measured at the ac pulse amplitude of 6.3 mV. (c) The Rabi oscillation measured for a longer rf pulse duration. The Rabi frequency is set at the center resonance frequency $f = 351 MHz$ . (d) Rabi oscillation power dependence. (e) Rabi frequencies extracted from the power dependence measurement. Each of the Rabi oscillations in Fig. 2 is fit by a sine curve $p_{↑ ↓} = A \sin (2 π f_{R} t - π / 2) + B$ , where $A$ and $B$ are the constants to account for the readout fidelities and $f_{R}$ is the Rabi frequency.
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Figure 3
Detuning dependence of the phase coherence time. (a) Detuning dependence of the phase coherence time measured by Ramsey interferometry. The error bars represent one sigma from the mean. The inset schematic shows the measurement sequence of the Ramsey interferometry. First, we apply a $π / 2$ pulse and wait for some time. Finally, the phase accumulated during the waiting time is projected to the $z$ axis by another $π / 2$ pulse. (b)–(e) Ramsey fringes measured at various detuning conditions. Each curve is fit by a Gaussian decaying oscillation and $T_{2}^{*}$ is extracted. The detuning values are 0 for (b), 20 for (c), 22.5 for (d), and 25 mV for (e).
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Figure 4
Randomized benchmarking measurement. The sequence fidelity $F (m)$ is defined as $F (m) = p_{↑ ↓}^{| ↑ ↓ ⟩} (m) - p_{↑ ↓}^{| ↓ ↑ ⟩} (m)$ , where $p_{↑ ↓}^{| ↑ ↓ ⟩} (m)$ ( $p_{↑ ↓}^{| ↓ ↑ ⟩} (m)$ ) is the probability of finding an $| ↑ ↓ ⟩$ state after applying the recovery Clifford gate designed to result in an ideal outcome $| \tilde{↑ ↓} ⟩$ ( $| \tilde{↓ ↑} ⟩$ ). The decay curve is fit by an exponential decay $F (m) = V p^{m}$ , where $V$ is the visibility. We obtain $V = 0.665 \pm 0.009$ and $p = 0.985 \pm 0.0009$ from the fit. The fitting errors represent one sigma from the mean.
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