Extended Data Fig. 7: Pulse sequences for coherent spin-valley-driven singlet-triplet oscillations.
a Pulse sequence for S − T− Rabi oscillations. We prepare the double dot in the state \(\left\vert {S}^{+-}\right\rangle\), pulse to different values of ϵ for a variable evolution time te, and then measure the singlet return probability PS by pulsing ϵ to the PSB region in (4,0). b Pulse sequence for S − T− Ramsey oscillations, with a 3π/2 and π/2 pulse performed at the ϵ value of the S − T− avoided crossing (denoted \({\Delta }^{S{T}_{-}}\)) before and after the evolution. Through a \({\Delta }^{S{T}_{-}}\) 3π/2 pulse, we prepare the double dot in a superposition of \(\left\vert {S}^{+-}\right\rangle\) and either \(\left\vert {T}_{-}^{--}\right\rangle\) or \(\left\vert {T}_{-}^{++}\right\rangle\), depending on which spin funnel we are operating near. Specifically, for the second spin funnel, we prepare \(\left\vert \psi \right\rangle =\frac{1}{\sqrt{2}}\)(\(\left\vert {S}^{+-}\right\rangle +i\left\vert {T}_{-}^{--}\right\rangle\)) and for the third spin funnel, we prepare \(\left\vert \psi \right\rangle =\frac{1}{\sqrt{2}}\)(\(\left\vert {S}^{+-}\right\rangle -i\left\vert {T}_{-}^{++}\right\rangle\)), if \({\Delta }_{1(2)}^{sv}\) are real and positive. After the evolution, we use a \({\Delta }^{S{T}_{-}}\,\)π/2 pulse to map \(\left\vert \psi \right\rangle\) to \(\left\vert {S}^{+-}\right\rangle\) for PSB readout. c Pulse sequence used to observe triplet-triplet oscillations, with a π pulse at the ϵ value of the S − T− avoided crossing before and after the evolution. Through a \({\Delta }^{S{T}_{-}}\,\)π pulse, we prepare the excited \(\left\vert {T}_{-}\right\rangle\) state, \(\left\vert {T}_{-}^{--}\right\rangle\) for the second spin funnel or \(\left\vert {T}_{-}^{++}\right\rangle\) for the third spin funnel. After the evolution, we apply another \({\Delta }^{S{T}_{-}}\,\)π pulse to map the excited \(\left\vert {T}_{-}\right\rangle\) state to \(\left\vert {S}^{+-}\right\rangle\) for PSB readout. d Control measurement at a magnetic away from the spin funnels, Bz=350 mT, using the pulse sequence in a. The energy level diagram for this magnetic field is displayed in Extended Data Fig. 2a, right panel. The two vertical lines in the data near ϵ=0 correspond to where \(\left\vert {T}_{-}^{+-}\right\rangle\) and \(\left\vert {T}_{-}^{--}\right\rangle\) come into resonance with \(\left\vert {S}^{+-}\right\rangle\), which occur at energies below the range plotted in Extended Data Fig. 2a.
