Indications of a soft cutoff frequency in the charge noise of a Si/SiGe quantum dot spin qubit

Characterizing charge noise is of prime importance to the semiconductor spin qubit community. We analyze the echo amplitude data from a recent experiment [Yoneda et al., Nat. Nanotechnol. 13, 102 (2018)] and note that the data show small but consistent deviations from a $1/f^{\alpha }$ noise power spectrum at the higher frequencies in the measured range. We report the results of using a physical noise model based on two-level fluctuators to fit the data and find that it can mostly explain the deviations. While our results are suggestive rather than conclusive, they provide what may be an early indication of a high-frequency cutoff in the charge noise. The location of this cutoff, where the power spectral density of the noise gradually rolls off from $1/f$ to $1/f^2$, crucial knowledge for designing precise qubit control pulses, is given by our fit of the data to be around 200 kHz.

Figure 1

Coherence function $W\left(t\right)$ as a function of total CPMG time $t$ in $\mu \mathrm{s}$, for CPMG different number $\pi$ pulses $n$. The blue line segments correspond to joined experimental $W\left(t\right)$ data points, orange dashed curves correspond to $W\left(t\right)=exp(-{[t/T_2\left(n\right)]}^{\alpha })$ predicted by the PSD ${\hslash }^2{A}_0^{1+\alpha }/{\omega }^{\alpha }$ with $\alpha =1.01$ and $T_2^0\approx 91\mu \mathrm{s}$, and green curves correspond to $W\left(t\right)$ corresponding to the PSD given in Eq. (5) with $v/2\pi \approx 2.65$ kHz, ${\gamma }_{\text{ir}}/2\pi =0.1$ kHz, and ${\gamma }_c/2\pi =200$ kHz.

Figure 2

Comparison of fitted PSD functions used in Fig. 1 in a frequency range from 0.1 kHz to 400 kHz. At the TLF cutoff frequency $\omega /2\pi ={\gamma }_c/2\pi =200$ kHz, $S_b$ becomes smaller than $S_{1/f}$ by a factor of $\approx 2$.