显性控制光格中粒子跨越混沌海的量子输运

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.

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。

本项目已运用项目组建立的基于联合调制和解析解的显性控制方法和已知优化控制方法，结合解析分析和数值计算，研究了混沌特性对操控具有任意格点数的低维光学晶格或超晶格中单粒子和玻色-爱因斯坦凝聚体(BEC)量子输运的影响，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。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，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。主要研究内容是： . 1） 基于一维光学晶格和超晶格中驱动单粒子的精确解和自旋-轨道耦合二分量BEC的微扰解和数值解，研究经典混沌参数区域和经典相空间混沌海中平均初始条件对显性操控量子输运的影响，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,揭示混沌辅助的量子输运规律。2）进一步研究作为经典混沌系统的少阱和多阱囚禁的少粒子系统中量子隧穿的相干控制，包括由周期驱动调制的空间非对称棘齿对量子隧穿动力学的影响以及对量子信息输运的应用。3）对于光晶格中受激光脉冲撞击的量子粒子这一典型的经典混沌系统，研究了Lamb-Dicke区域的量子运动，得到描述离子波包串的精确的广义相干态解及对应的经典和量子一致的稳定性参数区域，并揭示了这些结果对自旋-轨道纠缠的深刻影响。4）基于一类三维非线性混沌电路系统，我们探索混沌的鲁棒性、幅度调制及位置调制等特性，进而提出鲁棒混沌系统建模新方法。通过修正幅度控制因子及位置调制因子，提出构建多翅膀混沌系统的方案。以混沌系统幅度参数为加密密钥，设计了一种新型的图像加密方案。. 这些结果对于推进量子混沌学基础理论的发展及其在量子信息输运和处理以及BEC应用基础等方面具有实际意义。已有14篇相关论文发表在Phys. Rev.， Chaos 和 Sci. Rep.等国际著名期刊上, 并被SCI期刊文章广泛引用，获同行一致好评。