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Inverse engineering of electric fields has been recently proposed to achievefast and robust spin control in a single-electron quantum dot with spin-orbitcoupling. In this paper we design, by inverse engineering based onLewis-Riesenfeld invariants, time-dependent electric fields to realize fasttransitions in the selected singlet-triplet subspace of a two-electron doublequantum dot. We apply two-mode driving schemes, directly employing theLewis-Riesenfeld phases, to minimize the electric field necessary to designflexible protocols and perform spin manipulation on the chosen timescale.

Fast spin control in a two-electron double quantum dot by dynamical invariants