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

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