Superadiabatic Landau-Zener model and the valley transitions during electron shuttling in Si

The transition dynamics of two-state systems with time-dependent energy levels is one of the basic models in quantum physics and has been used to describe various physical systems. We propose here a generalization of the Landau-Zener (LZ) problem characterized by distinct paths of the instantaneous eigenstates as the system evolves in time, while keeping the instantaneous eigenenergies exactly as in the standard LZ model. We show that these paths play an essential role in the transition probability P between the two states, and can lead to a substantial reduction of P. We find that it is even possible to achieve P=0 in an instructive extreme case, as well as large P even in the absence of any anticrossing point. The superadiabatic LZ model can describe valley transition dynamics during charge and spin shuttling in semiconductor quantum dots and leads to strategies to enhance the valley shuttling fidelity that constitute a drastic improvement compared with previous strategies.