Fig. 2: Exchange control.
From: Bell-state tomography in a silicon many-electron artificial molecule
a, b Schematic showing the two different mechanisms to electrically control exchange coupling between quantum dots, by a voltage detuning between G1 and G2 gate, and b barrier control with J gate. c, d Examples of CZ oscillations controlled via c detuning or d J gate. We apply a pulse sequence X1 − CZ − X1, where X1 is a \(\frac{\pi }{2}\) rotation around the x-axis of Q1, then measure the probability of an odd spin parity Podd. Orange Roman numbers in each panel correspond to the applied voltage indicated in e–h, drawn as orange dashed lines. Blue and red markers correspond to the normalized measured Podd with Q2 initialized as \(\left|\downarrow \right\rangle\) or \(\left|\uparrow \right\rangle\), respectively. The data are fitted using the equation \({P}_{{\rm{odd}}}=\frac{A}{2}(1-\cos (2\pi {f}_{{\rm{osc}}}t){e}^{-t/{T}_{2}^{{\rm{CZ}}}})+b\). The Ramsey frequency fosc is displayed as blue or red text on the panel. In order to compensate the strong Stark shift induced by gate pulsing, we adopt different rotating frames, offset by a reference frequency fref between experiments, as presented in grey dashed curves behind each measurement data set. We extract the CZ frequency fCZ = fref + fosc in a common frame and the difference between \({f}_{{\rm{CZ}},{\rm{Q}}2 = \left|\downarrow \right\rangle }\) and \({f}_{{\rm{CZ}},{\rm{Q}}2 = \left|\uparrow \right\rangle }\), which gives the exchange coupling frequency J, shown as black bold text. e, f The oscillation frequency fCZ as a function of e detuning or f J gate control. Blue and red line corresponds to Q1 =  \(\left|\downarrow \right\rangle\) and \(\left|\uparrow \right\rangle\), respectively. g, h Extracted exchange oscillation frequency J. i Damping time \({T}_{2}^{{\rm{CZ}}}\) of the measured oscillations as a function of exchange coupling J, for Q2 = \(\left|\uparrow \right\rangle\) and for detuning (purple) and J gate control (green). j Quality factor \(Q=J\times {T}_{2}^{{\rm{CZ}}}\) as a function of J, extracted from i. Error bars represents ± 5% fitting error.
