On Some Model Problems in Quantum Control

Abstract

Control and manipulation of quantum mechanical systems using electromagnetic fields is a widely studied subject in areas of physics and chemistry, including spectroscopy, atomic molecular, and optical physics, and quantum chemistry. This article attempts to provide a glimpse into the rich class of bilinear control systems that are ubiquitous in these problems. In this article, we use control of spin systems in magnetic resonance as a model system to highlight characteristic feature of problems in quantum control. Background information is provided to enable the reader to appreciate new results and developments, where principled use of ideas from control theory have provided new insights into finding optimal ways to control and manipulate quantum mechanical systems. The study of deterministic and stochastic models that arise in problems in measurement and manipulation of quantum mechanical systems may foster new developments in control.