Fig. 3.

Exchange drive oscillations and individual electron ESR at low field. a Energy diagram for the five lowest energy states near the (0, 2)–(1, 1) anti-crossing represented in the spin basis. Compared to Fig. 2a, an increased magnetic field $B_0^z$ splits off polarized triplets $∣T_{\pm }⟩$ while δg due to the SO coupling breaks the $∣\left(1,1\right)S⟩\mathrm{∕}∣T_0⟩$ degeneracy producing δE_Z. b Bloch sphere representation of the $∣\left(1,1\right)S⟩\mathrm{∕}∣T_0⟩$ qubit showing effect of the Heisenberg exchange J and δE_Z c, d Coherent Rabi oscillations between $∣\downarrow \uparrow ⟩$ and $∣\uparrow \downarrow ⟩$ states, driven by exchange J. c Pulse sequence for data in d and e; adiabatic ramp (diabatic through the S_H/T₋ crossing) prepares $∣\downarrow \uparrow ⟩$ (assuming g₂ > g₁). Diabatic pulses back to the high exchange region then causes coherent evolution of the state for a period of variable time/depth. The resulting change in population of $∣\downarrow \uparrow ⟩$ is mapped back to $∣\left(0,2\right)S⟩$ using the inverse adiabatic ramp. d Fourier transform of time series e which shows exchange driven oscillations between the $∣\downarrow \uparrow ⟩$ and $∣\uparrow \downarrow ⟩$ states. f Pulse sequence used for data in g. g Triplet probability as a function of detuning ε and applied ESR frequency with f₀ = 4.205 GHz. ESR spin rotations of the spin in the left dot (upper branch) and right dot (lower branch), using an on-chip microwave ESR line. $∣\downarrow \uparrow ⟩$ is prepared similar to b, a 25 μs ESR pulse of varying frequency is applied rotating $∣\downarrow \uparrow ⟩\to ∣\uparrow \uparrow ⟩$ when $g_2{\mu }_{\mathrm{B}}{B}_0^z\mathrm{∕}h$ = f_ESR, and $∣\downarrow \uparrow ⟩\to ∣\downarrow \downarrow ⟩$, when $g_1{\mu }_{\mathrm{B}}{B}_0^z\mathrm{∕}h$ = f_ESR; $∣\downarrow \uparrow ⟩$ is again mapped back $∣\left(0,2\right)S⟩$. We find $∣g_2-g_1∣$ = (0.43 ± 0.02) × 10⁻³