Minimal time trajectories for two-level quantum systems with two bounded controls

Ugo Boscain, Fredrik Grönberg, Ruixing Long, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we treat the time-optimal control problem with techniques of optimal synthesis on 2D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the initial condition.

Original languageEnglish (US)
Article number062106
JournalJournal of Mathematical Physics
Issue number6
StatePublished - Jun 25 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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