Fig. 2
Mapping and control of singlet T− triplet anti-crossing. a Energy diagram for the five lowest energy states near the (0, 2)–(1, 1) anti-crossing represented in the singlet-triplet basis. b, c Five-level pulse sequence used in panels d, e and g. b A \(\left| {(0,2)S} \right\rangle \) state is initialised by moving from M, through point F where rapid tunnelling occurs with the reservoir, to point I. From point P, we plunge into the (1,1) region to probe the anti-crossing, and return via P to then move to the latched spin blockade measurement point at M. c Plunge depth into (1, 1) between P and ε as a function of time, illustrating experimental variables including ε detuning, ramp rates and dwell time. d A characteristic spin funnel is observed where the SH/T− state degeneracy results in a relaxation hotspot. e The SH/T− coupling strength Δ(θ) is characterized by performing a single passage Landau–Zener excitation experiment43 at two different \(B_0^z\) applied magnetic field settings. Here, the x-axis indicates the rate of change of the SH/T− energy separation as extracted from measurements of this energy difference vs. voltage and the voltage ramp rate into (1, 1). The increase of this rate (known as the energy level velocity ν) acts to preserve the \(\left| {S_{\mathrm{H}}} \right\rangle \) initial state following the Landau–Zener formula, to which we fit to extract \(\left| {{\mathrm{\Delta }}(\theta )} \right|\) (see text). Solid lines show the fit while shaded regions are a 95% confidence interval. Arrows indicate the energy level velocity used for given experiments. f Energy diagram representation for the effect of varying ramp rate νin with respect to Δ as in e while keeping νout diabatic. g Fourier transform of h Landau–Zener–Stueckelberg interference pattern produced by semi-diabatic double-passage through the S/T− anti-crossing under zero-field Bz offset
