Fig. 3: Compromise-free operation.
a Top: Experimental data of fRabi and g as a function of VL. Bottom: Dark blue circles show coherence times \({T}_{2}^{{{{\rm{Hahn}}}}}\) obtained from fits of the time-dependent readout current measured in Hahn-echo experiments at different voltages VL. Light blue circles show modeled coherence times taking into account \({g}_{i}^{{\prime} }({V}_{{{{\rm{L}}}}})\) from panels b–f using Eq. (2), yielding \({S}_{{{{\rm{G}}}}}\,=\,29\,{{{\rm{nV}}}}/\sqrt{{{{\rm{Hz}}}}}\). Vertical dashed line at VL = 1330 mV shows sweet spot, where \({T}_{2}^{{{{\rm{Hahn}}}}}\) is maximal. This spot coincides with fastest fRabi within experimental errors. Error bars correspond to standard deviations that result from fitting. Inset: Pairs of fRabi and \({T}_{2}^{{{{\rm{Hahn}}}}}\) from VL = 1330–1360 mV in 10 mV steps. b–f Show \({g}_{i}^{{\prime} }({V}_{{{{\rm{L}}}}}):=\partial g/\partial {V}_{{{{\rm{i}}}}}({V}_{{{{\rm{L}}}}})\), as a function of different static voltages on gate VL. Dark blue data represent values of VL for which \({g}_{i}^{{\prime} }({V}_{{{{\rm{L}}}}})\) were measured. Light blue line represents linearly interpolated data needed to match the number of measured data points between \({g}_{i}^{{\prime} }({V}_{{{{\rm{L}}}}})\) and \({T}_{2}^{{{{\rm{Hahn}}}}}\), which was fitted in (a). Vertical dashed line marks the sweet spot at VL = 1330 mV where all five \({g}_{i}^{{\prime} }({V}_{{{{\rm{L}}}}})\) reach near zero, defining the sweet spot. Horizontal dashed line marks the zero-line of the \({g}_{i}^{{\prime} }({V}_{{{{\rm{L}}}}})\). g The FACTOR: 2D voltage space showing \({T}_{2}^{{{{\rm{Hahn}}}}}\) as function of VM and VL. Filled circles represent measured coherence times \({T}_{2}^{{{{\rm{Hahn}}}}}\) extracted analogously to panel a. Data trace corresponding to the dark blue trace on panel a is referenced by the blue arrow on the 2D plot. An additional trace of \({T}_{2}^{{{{\rm{Hahn}}}}}\) as a function of VL for fixed VM = 630 mV is indicated by the vertical dark blue dashed line to the left end of the plot, as well as a trace of \({T}_{2}^{{{{\rm{Hahn}}}}}\) as a function of VM for fixed VL = 1320 mV which is indicated by the horizontal red dashed. Background is obtained by a Gaussian process interpolation serving as a guide to the eye. Black contours show a Gaussian process interpolation of measured Rabi frequencies, highlighting the overlap of maxima in \({T}_{2}^{{{{\rm{Hahn}}}}}\) and fRabi.
