Minimal time trajectories for two-level quantum systems with two bounded controls
Minimal time trajectories for two-level quantum systems with two bounded controls
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DOI：
10.1063/1.4882158
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发表时间：
2014-06-01
影响因子：
1.3
通讯作者：
Rabitz, Herschel
中科院分区：
文献类型：
--
作者：
Boscain, Ugo;Gronberg, Fredrik;Rabitz, Herschel
在本文中，我们考虑由两个有界振幅的外部场驱动的二级量子系统的最小时间布居迁移问题。这些控件被建模为真实函数，我们不使用旋转波近似。在布洛赫球上投影后，我们用二维流形上的最优综合技术来处理时间最优控制问题。基于庞特里亚金极大值原理，我们描述了一组有限的候选最佳轨迹。该组的特性对于完整的优化合成至关重要，通过数值模拟进行了说明。此外，当两个控制具有相同的界限并且该界限相对于两个能级的差异较小时，我们得到了直到初始条件对映点的小邻域的完整最优合成。 (C) 2014 AIP 出版有限责任公司。
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. (C) 2014 AIP Publishing LLC.