Fig. 3

Detuning dependence of oscillations. a Experimental mapping of the detuning dependence of the time domain oscillations; b Energy spectrum derived from fitting to the extracted dispersion: A two-dimensional color bar is used to simultaneously display a state’s makeup in the charge degree of freedom, calculated as the probability of a state, |ψ〉, being in the middle dot, |〈ψ|M〉|², and the valley degree of freedom, calculated as the probability of being in the first excited valley state conditional upon being in the left subspace, \(\frac{{{{\left| {\left\langle {\it{\psi }} \right|\left. {{{\rm{L}}_{{{\rm{v}}_{\rm{2}}}}}} \right\rangle } \right|}^2}}}{{1 - {{\left| {\left\langle {\it{\psi }} \right|\left. {\rm{M}} \right\rangle } \right|}^2}}}\). (δ = 5.57 GHz, Δ ₁ = 6.4 GHz, Δ ₂ = 13.6 GHz) c Simulated charge-sensing transconductance signal, obtained by solving the time-dependent Schrodinger equation without dissipation: A square pulse with a finite rise time of 200 ps was assumed. d Experimentally extracted frequencies plotted along with the separation between the lower two eigenenergies as a function of detuning: The extracted value of the valley splitting, δ, is plotted as a dotted line. The color of the fitted curve is the color associated with the middle eigenstate at a detuning using the coloring from b. Along the bottom axis, the color represents the makeup of the ground state