显性控制光格中粒子跨越混沌海的量子输运

项目名称： 显性控制光格中粒子跨越混沌海的量子输运

项目编号： No.11475060

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 海文华

作者单位： 湖南师范大学

项目金额： 82万元

中文摘要： 混沌系统最显著的特点是它的复杂性和敏感性，复杂性导致基于混沌柔韧性的测量应对优势，敏感性隐含高速安全操控系统的可能。本项目拟运用申请者建立的基于联合调制和精确解的显性控制方法和已知优化控制方法，研究混沌特性对操控具有任意格点数的低维光学晶格和超晶格中量子输运的影响。考虑对混沌初态的平均，设置对光格深度和斜度的各种联合调制，着重研究粒子通过跨越经典相空间混沌海来实现的量子输运。结合解析分析和数值计算，澄清以往关于混沌系统经典-量子对应原理破缺的困惑和混沌有助于量子隧穿或局域化的矛盾；提出显性控制粒子快速输运到相空间指定区域和局域化的方案，并设计某些新型量子器件。应用 Bloch小组近期报道的实验结果，把关于单粒子输运的结果推广到两内态多粒子相互作用系统，并进一步研究相关量子信息输运与处理的操控方案。所得结论对混沌特性的应用基础和量子输运与信息处理的研究有参考意义。

中文关键词： 显性控制；量子输运；混沌海；初始条件；联合调制

英文摘要： The most striking features of a chaotic system are its complexity and sensitivity. Complexity leads to the repartee advantage of measurement based on the chaotic flexibility, and sensitivity implies the possibility for controlling the system more secure at high speeds. This project aims at applying the transparent control method based on combined modulation and exact solutions established by the applicant and the well-known optimal control scheme to investigate the dependence of manipulating quantum transport for the particles in the low-dimensional optical lattices and superlattices with any site-number on the chaotic characteristics. Considering the average to the chaotic initial states and setting various combined modulations to depth and tilt of the optical lattices, we emphatically study the quantum transport through crossing the chaotic sea of classical phase space. Combining analytical and numerical calculations, the previous perplexity on the breakdown of the correspondence principle in a chaotic system and the contradiction of chaos-assisted tnneling or localization will be cleared. Several schemes for transparently controlling particle to rapidly transport and to localize at some given regions in the phase space will be provided, and some novel quantum devices will be designed. Applying the recent experimental results reported by Bloch group, we will extend the results of a single particle to some two-level many-body interacting systems, and explore the corresponding control schemes of quantum information transport and processing. The obtained conclusions could be referable to the application bases of the chaotic features and to the investigations on the quantum transport and information processing.

英文关键词： transparent control;quantum transport;chaotic sea;initial condition;combined modulation