Cancelling second order frequency shifts in Ge hole spin qubits via bichromatic control

Abstract

Germanium quantum dot hole spin qubits are compatible with fully electrical control and are progressing toward multi-qubit operations. However, their coherence is limited by charge noise and driving field induced frequency shifts, and the resulting ensemble $1/f$ dephasing. Here we theoretically demonstrate that a bichromatic driving scheme cancels the second order frequency shift from the control field without sacrificing the electric dipole spin resonance (EDSR) rate, and without additional gate design or microwave engineering. Based on this property, we further demonstrate that bichromatic control creates a wide operating window that reduces sensitivity to quasi-static charge noise and thus enhances single qubit gate fidelity. This method provides a low-power route to a stabler frequency operation in germanium hole spin qubits and is readily transferable to other semiconductor spin qubit platforms.

Figures (3)

• Figure 1: Heatmap of the second order frequency shift $\delta\omega^{(2)}$ as a function of the two driving frequencies $\omega_1$ and $\omega_2$. The parameters used to generate this figure are $E_{\text{gate}}=10$ MV/m, $B_x=1$ T, and $E_1=E_2=10$ kV/m. The dashed black contour indicates $\delta\omega^{(2)}=0$. Grey shaded regions denote parameter regimes associated with multiphoton processes and are therefore excluded from the analysis. The green highlighted region indicates the fast EDSR regime.
• Figure 2: $R_0$ versus the auxiliary frequency $\omega_2$ at $\omega_1=\omega_0$. The two dashed lines indicate the frequency thresholds for $R_0<0$, which set the minimum auxiliary frequency.
• Figure 3: Dephasing rate $1/T_2^*$ versus auxiliary frequency $\omega_2$ under bichromatic driving at $\omega_1=\omega_0$ to maintain a fast Rabi rate. Blue solid circles: $E_{\text{gate}}=5$ MV/m; red dashed squares: $E_{\text{gate}}=10$ MV/m. The horizontal lines indicate the baseline dephasing rates under single tone driving for the same $\omega_1=\omega_0$ and $E_1$; the solid blue (dashed red) line corresponds to $E_{\text{gate}}=5$ and $10$ MV/m respectively. Parameters are taken from Ref. Abhik2023. Typical $T_2^*$ values in this range are $3-6~\upmu\mathrm{s}$ (lower $1/T_2^*$ is better).