How fast can quantum brachistochrone evolve?

The quantum speed limit (QSL) represents the cornerstone of essential physical limit on the speed of evolution process in quantum mechanics. To derive the QSL for arbitrary quantum systems, here we present a geometric method, which is estiblished on the quantum brachistochrone characterized by the Riemannian metric. As an application to the complex quantum system, we consider the nonlinear Landau-Zener type two-level system, representing coherent atoms for BECs with mean-field interaction. The analytical expression of the quantum brachistochrone and population are obtained for the nonlinear system. We further derive the corresponding optimal procotol and demonstrate that the QSL is tight. We also generalize our formulation to open quantum systems.
Comment: 5+3 pages,1+1 figures