Control of Quantum Systems
The control of quantum systems has many applications, ranging from coherent spectroscopy to quantum information processing. In most applications, the system of interest is not isolated but interacts with its environment. This leads to the phenomenon of relaxation, which in practice results in signal loss and ultimately limits the range of applications. The goal of our research is the manipulation of quantum systems in a manner that minimizes relaxation losses. Specifically, for each system we want to calculate the theoretical upper limit for the coherence transfer efficiency in the presence of relaxation and to develop optimal controls (pulse sequences) that achieve this limit experimentally.
From a control theory point of view, the above problems give as the physical motivation to study a new class of control systems that are linear in state and are characterized by the fact that the original controls can be expressed as polynomial functions of some new control parameters. Up to now, our research has been focused in the control of coupled spin dynamics in nuclear magnetic resonance (NMR) spectroscopy in liquids. We have developed relaxation optimized pulse elements that in many cases of practical interest give much better efficiency than the conventionally used pulse sequences, for example INEPT. The methods developed are by no means restricted to NMR applications but are broadly applicable to coherent control of quantum-mechanical phenomena in presence of dissipation.