Enhancement of Electric Drive in Silicon Quantum Dots with Electric Quadrupole Spin Resonance

TL;DR

The paper addresses the challenge that Electric Dipole Spin Resonance (EDSR) fails to account for observed fast Rabi oscillations in multi-electron silicon quantum dots. It introduces Electric Quadrupole Spin Resonance (EQSR) by adding a quadrupole driving term $Q_{xy}$ to the driving Hamiltonian, yielding $H_{AC}(t) = |e|E_y y \cos(\omega t) + |e|Q_{xy} xy \cos(\omega t)$ and a Rabi frequency $\hbar \Omega = |\langle 0| e E_y y + e Q_{xy} xy |1\rangle|$, with enhancements tied to intrinsic spin-orbit couplings via $|b_i| \propto \alpha^2 - \beta^2$ near orbital degeneracy. In 5e and 13e silicon dots, EQSR captures the Rabi-speedups and the nonlinear dependence of qubit frequencies on dot ellipticity, offering a mechanism for fast, localized spin control that could reduce reliance on micromagnets. The results suggest that combining EQSR with intrinsic spin-orbit coupling provides a scalable path for coherent spin manipulation in multi-electron quantum dots, and point to future work including valley-orbit coupling and electron–electron interactions.

Abstract

Quantum computation with electron spin qubits requires coherent and efficient manipulation of these spins, typically accomplished through the application of alternating magnetic or electric fields for electron spin resonance (ESR). In particular, electrical driving allows us to apply localized fields on the electrons, which benefits scale-up architectures. However, we have found that Electric Dipole Spin Resonance (EDSR) is insufficient for modeling the Rabi behavior in recent experimental studies. Therefore, we propose that the electron spin is being driven by a new method of electric spin qubit control which generalizes the spin dynamics by taking into account a quadrupolar contribution of the quantum dot: electric quadrupole spin resonance (EQSR). In this work, we explore the electric quadrupole driving of a quantum dot in silicon, specifically examining the cases of 5 and 13 electron occupancies.

Figures (4)

• Figure 1: Schematic of p-orbital-like states. As the ellipticity of the electrostatic potential decreases, SOC hybridization of the orbital and spin characters of the states increases, forming a spin-orbit qubit. $\mathcal{E}_\text{Zee}$ is the Zeeman splitting.
• Figure 2: Ellipticity and orbital energies. (a) Plot of the extracted orbital excitation energies $\mathcal{E}_{x(y)}=\hbar\omega_{x(y)}$ against $V_\mathrm{G2}$ via real-space simulations of the single particle states given an electrostatic potential simulated with COMSOL. (b) Plot of the ellipticity of the dot $\delta \equiv \frac{\mathcal{E}_{x}}{\mathcal{E}_{y}}$ against $V_\mathrm{G2}$ for the 5e configuration in Figs. 3(g-i) and 13e configuration in Figs. 3(j-l) of Ref. leon2020coherent. Linear slopes are also shown. Ellipticities were obtained from calculations of energies shown in (a).
• Figure 3: Cartoon of the effects of dipolar and quadrupolar electric fields. An AC quadrupole field results in a dilation/contraction of the electrostatic potential in orthogonal axes whereas an AC dipole electric field results in a shift.
• Figure 4: Fitted EQSR model. (a) Energies of the $P_x$ and $P_y$ orbitals with the lowest two being the ones driven by EQSR. (b) Qubit frequency spectrum of the 5 electron regime, with the measured data in black and the fitted line in red. (c) Rabi frequency measured in the 5 electron regime, with the measured data in black and the fitted line in blue. The dashed line indicates the model prediction if only the electric dipole effect is accounted for. (d) Energies of the $D$ orbitals, with the lowest two being those driven by EQSR. (e) Qubit frequency spectrum of the 13 electron regime, with the measured data in black and the fitted line in red. (f) Rabi frequency measured in the 13-electron regime, with the measured data in black and fitted line in blue. The dashed line indicates the model prediction if only the electric dipole effect is accounted for. All $x$-axis labels here are the ellipticity $\delta \equiv \frac{\mathcal{E}_{x}}{\mathcal{E}_{y}}$.