Nonlinear two-level Landau-Zener type equations for systems with relevance for Bose-Einstein condensates and nonlinear optics are considered and the minimal time $T_{\min }$ to drive an initial state to a given target state is investigated. Surprisingly, the nonlinearity may be canceled by a time-optimal unconstrained driving and $T_{\min }$ becomes independent of the nonlinearity. For constrained and unconstrained driving explicit expressions are derived for $T_{\min }$, the optimal driving, and the protocol.

• Received 10 November 2015
• Revised 28 March 2016

DOI:https://doi.org/10.1103/PhysRevA.94.023624