High-Speed Driving of a Two-Level System
arXiv:1407.6502 · doi:10.1103/PhysRevA.90.032110
Abstract
A remarkably simple result is found for the optimal protocol of drivings for a general two-level Hamiltonian which transports a given initial state to a given final state in minimal time. If one of the three possible drivings is unconstrained in strength the problem is analytically completely solvable. A surprise arises for a class of states when one driving is bounded by a constant and the other drivings are constant. Then, for large , the optimal driving is of type bang-off-bang and for increasing one recovers the unconstrained result. However, for smaller the optimal driving can suddenly switch to bang-bang type. It is also shown that for general states one may have a multistep protocol. The present paper explicitly proves and considerably extends the author's results contained in Phys. Rev. Lett. {\bf 111}, 260501 (2013).
10 pages, 4 figures, typos corrected
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