Minimal time trajectories for two-level quantum systems with two bounded controls. (English) Zbl 1305.81089
Summary: 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.{
©2014 American Institute of Physics}
©2014 American Institute of Physics}
MSC:
| 81Q93 | Quantum control |
| 81V80 | Quantum optics |
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
| 68U20 | Simulation (MSC2010) |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
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