Control of the decoherence of open small quantum systems for applications in NMR and in quantum computation

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The project aims at the development of techniques for an effective decoupling of a small quantum system (spin 1/2 or quantum bit) from its environment which causes decoherence. The starting point is the technique of dynamical decoupling and the implementation of control pulses for the suppression of decoherence. We will develop and improve sequences and shapes of control pulses in order to prolong the coherence time of the small quantum system for applications in high-precision NMR and in quantum information processing. Three main goals will be pursued. One is the optimization of the sequence of pulses, i.e., the instants, at which control pulses are applied, are chosen such that decoherence is suppressed as well as possible. The other is to design the pulse shapes, i.e., the time-dependence of amplitudes and the time-dependence of the axes of rotation, such that the coupling to the environment has as small as possible a detrimental effect. Both goals depend on each other so that a particular focus is to design sequences of pulses of finite duration. The third goal is to extend the concept of optimized sequences and shapes of coherent control pulses also to quantum gates of two quantum bits (two spins). This step addresses a key element of quantum information processing.Technically, analytical expansions in the shortness of the pulses and/or of the sequences will be used as well as average Hamiltonian theory. The applicability of the analytical tools will be thoroughly checked by numerical simulations of spins coupled to various generic realizations of decoherence baths.