Ge hole spin control using acoustic waves

Abstract

Germanium hole spin qubits based on strained Ge/SiGe quantum well have attracted much research attention due to the strong spin-orbit coupling. In particular, the strain dependence of the heavy-hole--light-hole mixing and thus the $g$-tensor anisotropy offer unique opportunities for acoustic driving and spin-phonon coupling. In this work we numerically simulate the coherent control of a Ge hole spin using surface acoustic waves. The periodic strain dynamically modulates the $g$-tensor matrix and causes fast spin rotation under a small acoustic amplitude. Moreover, we show a strong anisotropy and confinement dependence of the Rabi frequency coming from the phase-shifted longitudinal and shear strain components. Our work lays the foundations for acoustic-driven spin control and spin-phonon coupling using Ge hole spin qubits.

Figures (5)

• Figure 1: Device architecture. Schematic of the Ge hole spin qubit driven by a surface acoustic wave. An interdigital transducer (IDT), fabricated on a ZnO film, generates a surface acoustic wave (SAW) propagating along the $[100]$ direction. The strain modulates the LH-HH mixing, causing the oscillating spatial profile of the $g$-tensor (represented by the shaking peanut shape).
• Figure 2: SAW-driven spin control. Time-resolved Rabi oscillation driven by the surface acoustic wave. The qubit is initialized in the ground state at $B = 0.396$ T, $\phi = 330^\circ$. The clear sinusoidal population transfer confirms coherent control via strain-induced $g$-tensor modulation.
• Figure 3: Time-dependent modulation of the $g$-tensor. Calculated variation of the $g$-tensor components $\Delta g_{ij}(t)$ under the influence of the SAW strain over one acoustic period. The distinct phase shift between $\Delta g_{zx}$ and ($\Delta g_{xx}, \Delta g_{yy}$) is the origin of the elliptical polarized driving mechanism.
• Figure 4: Anisotropy and chirality of SAW driving. (a) Rabi frequency $\Omega_R/2\pi$ as a function of the in-plane magnetic field angle $\phi$. The dots represent full numerical simulation results, while the dashed red line shows the excellent agreement achieved using the effective $g$-tensor modulation model. (b), (c) The left panel shows the trajectories of spin state (blue) and the effective driving vector (red) on the Bloch sphere evolved over the same time duration for $\phi = 330^\circ$ (green diamond in (a)) and $\phi = 30^\circ$ (red square in (a)), respectively. The right panel shows the ellipses projected on the x-y plane. The driving vector is elliptically polarized due to the intrinsic phase difference between the SAW strain components. At the optimal angle $\phi = 330^\circ$ (b), the effective vector co-rotates with the hole’s Larmor precession, maximizing the Rabi frequency. At $\phi = 30^\circ$ (c), it counter-rotates, suppressing the driving.
• Figure 5: Rabi frequency dependence on the dot geometry. Calculated Rabi frequency $\Omega_R/2\pi$ as a function of the SAW displacement amplitude $U$ at $\phi = 0^\circ$ for various dot dimensions $(L_x, L_y)$. The solid lines represent linear fits, confirming that the driving mechanism is governed by first-order strain coupling. The variation in slopes illustrates the impact of dot geometry on driving efficiency.