Phase-Driving Hole Spin Qubits

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Phase-Driving Hole Spin Qubits

Stefano Bosco, Simon Geyer, Leon C. Camenzind, Rafael S. Eggli, Andreas Fuhrer, Richard J. Warburton, Dominik M. Zumbühl, J. Carlos Egues, Andreas V. Kuhlmann, and Daniel Loss

Phys. Rev. Lett. 131, 197001 – Published 7 November 2023

Abstract

The spin-orbit interaction in spin qubits enables spin-flip transitions, resulting in Rabi oscillations when an external microwave field is resonant with the qubit frequency. Here, we introduce an alternative driving mechanism mediated by the strong spin-orbit interactions in hole spin qubits, where a far-detuned oscillating field couples to the qubit phase. Phase-driving at radio frequencies, orders of magnitude slower than the microwave qubit frequency, induces highly nontrivial spin dynamics, violating the Rabi resonance condition. By using a qubit integrated in a silicon fin field-effect transistor, we demonstrate a controllable suppression of resonant Rabi oscillations and their revivals at tunable sidebands. These sidebands enable alternative qubit control schemes using global fields and local far-detuned pulses, facilitating the design of dense large-scale qubit architectures with local qubit addressability. Phase-driving also decouples Rabi oscillations from noise, an effect due to a gapped Floquet spectrum and can enable Floquet engineering high-fidelity gates in future quantum processors.

Received 18 March 2023
Accepted 3 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.197001

Physics Subject Headings (PhySH)

Noise Quantum gates Quantum information with solid state qubits Quantum protocols

Field-effect transistors Floquet systems Nanowires Quantum dots

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Stefano Bosco ^1,*, Simon Geyer ¹, Leon C. Camenzind ^1,†, Rafael S. Eggli ¹, Andreas Fuhrer², Richard J. Warburton¹, Dominik M. Zumbühl ¹, J. Carlos Egues ^1,3, Andreas V. Kuhlmann ¹, and Daniel Loss¹

¹Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
²IBM Research Europe-Zurich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland
³Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil

^*stefano.bosco@unibas.ch
^†Present address: RIKEN, Center for Emergent Matter Science (CEMS), Wako-shi, Saitama 351-0198, Japan.

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Issue

Vol. 131, Iss. 19 — 10 November 2023

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Images

Figure 1
(a) Schematic of our phase-driven qubit. A hole spin qubit in a Si FinFET with Zeeman field $b$ is simultaneously driven by a microwave Rabi drive (blue) with amplitude $λ_{x}$ and frequency $ω_{x} \approx ω_{q} = | b | / ℏ$ and a radio-frequency phase drive (red) with amplitude $λ_{z}$ and frequency $ω_{z} ≪ ω_{q}$ . (b),(c) Phase-driving-induced slowdown of Rabi oscillations in qubit 1 (Q1). (b) We sweep $ω_{z}$ and measure the Pauli-spin-blockaded current $I_{norm}$ normalized by the maximal current, proportional to the spin-flip probability, for different burst times $t_{b}$ . The two regular Rabi peaks for $Z = λ_{z} / ω_{z} ≲ 0.4$ curve up and thus slow down for increasing $Z ≳ 0.4$ , following $ω_{R} = λ_{x} J_{0} (2 Z)$ . At larger $Z$ ’s the peaks split up and higher harmonics result in nontrivial features that are captured by the simulation in (c) obtained from Eq. (1) with $λ_{x} / 2 π = 29 MHz$ , $λ_{z} / 2 π = 30 MHz$ , and $ω_{q} / 2 π = ω_{x} / 2 π = 4.5 GHz$ .
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Figure 2
Sideband Rabi oscillations in qubit 2 (Q2). (a)–(c) Spin precession for simultaneous microwave Rabi driving and radio-frequency phase-driving against burst time $t_{b}$ and detuning $Δ$ . We show results for $Z = 0$ , $Z = 0.3$ , and $Z = 1.2$ . The typical chevron pattern centred at $Δ = 0$ in (a) is modified in (b),(c) by additional sidebands at $Δ / 2 π = \pm n \cdot ω_{z} / 2 π = \pm n \cdot 40 MHz$ and $\pm n \cdot 20 MHz$ , respectively. The $Δ = 0$ oscillations are slower in (b) and completely vanish in (c). (d)–(f) Simulations of the time evolution governed by Eq. (1), showing excellent agreement with experiments. We use $ω_{q} / 2 π = 4.95 GHz$ , $λ_{x} / 2 π = 10 MHz$ for the three $Z$ values and $λ_{z} = 0$ , $λ_{z} / 2 π = 0.3 ω_{z} / 2 π = 12 MHz$ , $λ_{z} / 2 π = 1.2 ω_{z} / 2 π = 24 MHz$ for (d)–(f), respectively.
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Figure 3
(a) Simulated phase-driving-induced undamped Rabi oscillations at $ω_{z} = λ_{x}$ . Black (red) dots denote Rabi probability averaged over $N = 10^{3}$ realizations of the noise Hamiltonian $H_{N}$ for $λ_{z} = 0$ ( $λ_{z} = 0.3 ω_{z}$ ) picked from a Gaussian distribution with zero mean and standard deviation $\bar{σ} = 0.05 ℏ ω_{z}$ . (c) Noisy Rabi oscillation at $Z = 1.2$ and various $λ_{x} / ω_{z}$ ratios. For reference, we show the gray dashed line, corresponding to the red line in (a). (b),(d) Floquet spectra against $λ_{x} / ω_{z}$ . (b) Solid black (red) dots show numerically computed Floquet energies $ω_{F}$ at $λ_{z} = 0$ ( $λ_{z} = 0.3 ω_{z}$ ); the lines denote the approximation in Eq. (4). Magenta (cyan) circles exhibit the probability $| c_{↓} |^{2} = | ⟨ ↓ | 0_{F} ⟩ |^{2}$ for a two-tone relative phase $φ = 0$ ( $φ = π / 2$ ). Dashed lines show Eq. (5). (d) Blue dots show the Floquet spectrum at $Z = 1.2$ , while the lines display the fitting formula $ω_{F}^{0, 1} = \pm ω_{z} [0.084 (λ_{x} / ω_{z})^{3} - 0.022 (λ_{x} / ω_{z})^{4}] mod (ω_{z})$ . We use $ω_{q} = 10^{3} ω_{z}$ .
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