Fig. 4: Phonons as possible decoherence source.
a Measured dephasing rate γ as a function of in-plane angle α (purple). The experimental data is plotted as purple points, and the error bar is given by a purple stripe. The error bars are dominated by the error associated with the gate-lever arm uncertainty. The black curve is the numerically calculated relaxation rate \({\gamma }_{1}^{{{{\rm{ph}}}}}(\alpha )\) originating from deformational phonons (see Section Decoherence). b Analytical relaxation rate \({\gamma }_{1}^{{{{\rm{ph}}}}}(\omega )\) as function of phonon frequency ω (see Equation (27) in Supplementary for details). The TLS operates in the frequency range as indicated with a negative slope of \({\gamma }_{1}^{{{{\rm{ph}}}}}(\omega )\). This explains the anti-correlation between the SOI gap Δso and the dephasing rate γ - a possible reason for the compromise-free sweet spot formation.
