Optimal control of a symmetric double quantum-dot nanostructure: Analytical results

Abstract

We study the potential for optimal control of a symmetric double quantum-dot structure interacting with a single pulsed electromagnetic field. We first use the rotating wave and resonant approximations and reduce the dynamics of the system to that of a degenerate three-level $\ensuremath{\Lambda}$-type system. We also formulate the optimal control problem in terms of differential equations that have to be fulfilled by the optimal electromagnetic fields. We then obtain general analytical expressions for the optimal pulse shapes that lead to global maximization of the final population of the target state and of the time-averaged population of the target state in the quantum-dot structure.