Efficient control of molecular rotations — time and controllability

在这个项目中，我们试图阐明时间在量子控制中的作用，使用分子旋转作为测试平台的重要基准。量子控制是指利用外部电磁场在原子或分子尺度上操纵动力学过程的能力。典型的控制任务需要最少的时间来执行，并且考虑到实际应用和基本理解，估计这个时间是重要的。迄今为止，除了少数例外情况外，这些估计只能凭经验得出。我们将利用可控性分析来解决时间在量子控制中的作用，将分子旋转控制的物理直觉与数学方法的最新进展相结合。我们的目标有三个方面：(i)我们寻求在与外部场相互作用的摄动处理的情况下确定可控性的条件；时间会通过摄动顺序自然出现。（ii）我们的目标是通过在伽辽金近似中对系统演化进行适当的分解来计算可控直径，从而计算控制的最小时间。（iii）我们将确定在量子控制中发生颤振现象的条件，颤振现象是指在有限时间间隔内无限次切换外场的病理情况。我们的提案建立在联合和跨学科工作的良好记录以及法国和德国合作伙伴在量子控制方面的长期专业知识的基础上，将数学方法的开创性发展与AMO物理学前沿的成功控制演示相结合。如果成功，我们的项目将提供一种系统的方法来确定量子控制的最小时间，并提高我们对实际量子控制是否以及如何受到数学病理影响的基本理解。对于我们的分子旋转测试平台，它将为控制开辟新的途径-与从超快分子物理到基础物理或基于分子的量子信息科学测试的应用相关。

In this project, we seek to elucidate the role of time in quantum control, using the important benchmark of molecular rotations as testbed. Quantum control refers to the ability to manipulate dynamical processes at the atomic or molecular scale using external electromagnetic fields. Typical control tasks require a minimum time to be carried out, and estimating this time is important in view of both practical applications and fundamental understanding. To date, these estimates can only be obtained empirically, save for a few exceptional cases. We will leverage controllability analysis to tackle the role of time in quantum control, combining physical intuition from the control of molecular rotations with recent advances of mathematical methods. Our goals are three-fold: (i) We seek to identify the conditions for controllability in case of a perturbative treatment of the interaction with the external fields; time will emerge naturally via the perturbation order. (ii) We aim to compute the controllability diameter, and thus the minimum time for control, by suitable decompositions of the system evolution in Galerkin approximations. (iii) We shall determine the conditions under which the chattering phenomenon, referring to the pathological case of an infinite number of times an external field is switched in a finite time interval, occurs in quantum control. Our proposal is built on a proven track record of joint and interdisciplinary work and the long-standing expertise of the French and German partners in quantum control, combining pioneering development of mathematical methods with successful demonstrations of control at the forefront of AMO physics. If successful, our project will provide a systematic approach to determine the minimum time for quantum control and improve our fundamental understanding of whether and how practical quantum control is affected by a mathematical pathology. For our testbed of molecular rotations, it will open new routes for control-relevant to applications from ultrafast molecular physics to tests of fundamental physics or molecule-based quantum information science.