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Coherent Destruction of Tunneling in a Two Electron Double Quantum Dot: Interplay of Coulomb interaction, spin-orbit interaction and AC field

We study a double quantum dot system with two interacting electrons in the presence of a time-dependent periodic (AC) electric field and spin-orbit interaction. We focus on the phenomenon of Coherent Destruction of Tunneling (CDT) for an initially localized state. Because of the periodicity introduced by the AC field we use Floquet theory to find quasi energies with their crossing and anti-crossing points corresponding to CDT . We observe that the AC field rescales the spin orbit and hopping amplitudes in terms of Bessel functions. The zeros of the Bessel functions are of the form of a ratio of AC field strength to its frequency and quasi energies at these points form anti-crossings in our case. We first prepare the system in a triplet state and study the evolution of its probability in the presence of spin-orbit interaction alone. We observe an oscillatory behavior which indicates spin flip transitions. However when the AC field is turned on the probability oscillations are highly suppressed at anti-crossing points leading to localization of initial state and the state retains its memory of spin even in the presence of spin flip interaction.