Fundamental mechanisms and obstacles in the bilinear control of Schrödinger equations

点击翻译按钮获取中文摘要

Quantum engineering is an emerging discipline with the potential of fundamentally (re-)shaping our technological and economic universes. It deals with the controlled manipulation of physical systems which are governed by the laws quantum mechanics. Its applications range from precision measurement devices, over crypto systems, to the iconic quantum computer. A solid grasp of quantum systems and their control will soon be part of the standard arsenal of engineers. This research program aims to identify some fundamental mathematical principles of quantum control to help develop a robust intuition about controlled quantum systems. The phenomena that will be studied include the role of dispersion in the control process and semiclassical approximations of the quantum dynamics. Motivated by the observation that a fair share of our intuition about quantum systems is derived from a few simple textbook systems that can be treated explicitly, the focus will be on simple one-dimensional systems, such as the infinite square well and the harmonic oscillator.