Extended Data Fig. 4: Measurement of the sign of ΔEZ = g1μBBz − g2μBBz.
a, Charge stability diagram of the (3,1) charge region illustrating the pulse positions for the relevant measurements. After adiabatically preparing either \(\left\vert {\downarrow }^{+}{\uparrow }^{-}\right\rangle\) or \(\left\vert {\uparrow }^{+}{\downarrow }^{-}\right\rangle\), we ramp V1 and V2 near either the dot-1 or dot-2 charge transitions (yellow lines) and wait for a variable time. We then reverse the pulse sequence and use PSB to distinguish between singlet and triplet states. b, Schematic of the relevant energy levels during relaxation near the dot-1 transition. Here, \(\left\vert {\uparrow }^{+}{\downarrow }^{-}\right\rangle\) may relax to \(\left\vert {\downarrow }^{-}{\downarrow }^{-}\right\rangle\) or \(\left\vert {\downarrow }^{+}{\downarrow }^{-}\right\rangle\) via exchange with (2,1) states. \(\left\vert {\downarrow }^{+}{\uparrow }^{-}\right\rangle\) cannot transition to any of \(\left\vert {T}_{-}^{+-}\right\rangle\), \(\left\vert {T}_{-}^{--}\right\rangle\), or \(\left\vert {T}_{-}^{++}\right\rangle\) without undergoing, at minimum, a spin flip in dot 2 and therefore does not appreciably relax during the microsecond timescales in these measurements. c, Schematic of the relevant energy levels during relaxation near the dot-2 transition. Here, \(\left\vert {\downarrow }^{+}{\uparrow }^{-}\right\rangle\) may relax to \(\left\vert {\downarrow }^{+}{\downarrow }^{+}\right\rangle\) or \(\left\vert {\downarrow }^{+}{\downarrow }^{-}\right\rangle\) via exchange with (3,0) states. \(\left\vert {\uparrow }^{+}{\downarrow }^{-}\right\rangle\) cannot transition to \(\left\vert {T}_{-}^{+-}\right\rangle\), \(\left\vert {T}_{-}^{--}\right\rangle\), or \(\left\vert {T}_{-}^{++}\right\rangle\) without incurring a spin flip in dot 1, and therefore does not appreciably relax. d, Triplet return probability near the dot-1 transition, corresponding to b. When preparing the higher-energy state, there is a slight enhancement in the triplet return probability inside the (3,1) region, suggesting that we have prepared the state \(\left\vert {\uparrow }^{+}{\downarrow }^{-}\right\rangle\). e, Triplet return probability near the dot-2 transition, corresponding to c. When preparing the lower-energy state, there is a strong enhancement in the triplet return probability inside the (3,1) region, indicating that we have prepared the state \(\left\vert {\downarrow }^{+}{\uparrow }^{-}\right\rangle\). The overall visibility of the higher-energy state traces is lower due to imperfections in the preparation and readout. We suspect that the stronger enhancement in the triplet return probability observed near the dot 2 transition compared to the enhancement observed near the dot 1 transition in d may be due to the details affecting the relaxation rates between the states involved in the relaxation processes. f, Plot of the triplet return probability for the high-energy-state measurement, \({P}_{T}^{e}\), minus the triplet return probability of the low-energy-state measurement, \({P}_{T}^{g}\), as a function of the wait time and wait position near the dot-1 transition. g, Plot of \({P}_{T}^{e}-{P}_{T}^{g}\) as a function of the wait time and wait position near the dot-2 transition. From the data shown in d-g, we conclude that the low-energy state is \(\left\vert {\downarrow }^{+}{\uparrow }^{-}\right\rangle\), and therefore ΔEZ > 0. All data shown in this figure are acquired at Bz=600 mT.
