A remarkably simple result is derived for the minimal time $T_{\min }$ required to drive a general initial state to a final target state by a Landau-Zener-type Hamiltonian or, equivalently, by time-dependent laser driving. The associated protocol is also derived. A surprise arises for some states when the interaction strength is bounded by a constant $c$. Then, for large $c$, the optimal driving is of type bang-off-bang and for increasing $c$ one recovers the unconstrained result. However, for smaller $c$ the optimal driving can suddenly switch to bang-bang type. We discuss the notion of quantum speed limit time.

• Received 27 May 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.260501