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

该项目旨在开发小量子系统（自旋1/2或量子比特）与其环境有效解耦的技术，从而导致退相干。本文的出发点是动态解耦技术和控制脉冲的实现来抑制退相干。我们将开发和改进控制脉冲的序列和形状，以延长小量子系统的相干时间，用于高精度核磁共振和量子信息处理。将追求三个主要目标。一种是脉冲序列的优化，即，选择施加控制脉冲的瞬间，使退相干尽可能地受到抑制。另一种是设计脉冲形状，即振幅的时间依赖性和旋转轴的时间依赖性，使其对环境的耦合具有尽可能小的有害影响。这两个目标都是相互依赖的，因此设计有限持续时间的脉冲序列是一个特别的重点。第三个目标是将相干控制脉冲的优化序列和形状的概念扩展到两个量子比特（两个自旋）的量子门。这一步解决了量子信息处理的一个关键要素。从技术上讲，脉冲和/或序列的解析展开式将与平均哈密顿理论一样被使用。分析工具的适用性将通过耦合到各种退相干槽的一般实现的自旋的数值模拟来彻底检查。

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.