Theory of Manipulation of Quantum System by Use of Nonadiabatic Quantum Phase

(1)我们提出了一种利用关联朗道-齐纳隧穿操纵量子比特的方法，其中两个非绝热能级交叉之间跃迁路径的干涉效应产生所需的么正变换。(2)对一类多水平交叉问题，给出了生存概率的精确表达式。采用形式微扰展开技术得到了解析结果。将所得公式应用于声子或自旋环境影响下的能级交叉问题的分析。(3)利用李代数模型揭示了隧穿相干破坏（CDT）与动态局域化（DL）之间的内在联系。两态动力学被映射到双模Schwinger玻色子模型的动力学上。DL被解释为CDT在操作员级别的无限大维度表示。(4)结合纳米技术和量子动力学的发展，综述了Landau-Zener类模型的研究进展。

(1) We proposed a method of manipulation of qubit by use of correlated Landau-Zener tunneling, in which the interference effect of transition paths between the two nonadiabatic level-crossings gives rise to desired unitary transformations.(2) An exact expression of the survival probability is obtained for a class of multi-level crossing problem. The formal perturbation expansion technique has been used successively to get the analytical result. The obtained formula has been applied to the analysis of the level-crossing problem under the effect of environment composed of phonons or spins.(3) The internal relationship between the coherent destruction of tunneling (CDT) and the dynamic localization (DL) has been made clear by the Lie algebraic model. The two-state dynamics is mapped on the dynamics of the two-mode Schwinger boson model. The DL is interpreted as an infinitely large dimensional representation of the CDT in the operator level.(4) The recent development in the study of the Landau-Zener-like model is reviewed in the light of advances in nano technologies and quantum dynamics.