超冷原子分子系统绝热几何相位研究

项目名称： 超冷原子分子系统绝热几何相位研究

项目编号： No.11305120

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 栗生长

作者单位： 西安交通大学

项目金额： 22万元

中文摘要： Berry相位(BP)是量子力学的重要概念之一，是量子绝热理论的重要组成部分。近年来，BP在量子信息处理和量子计算机设计中表现出了重要的应用价值。借助几何手段进行量子信息处理主要是利用BP固有的容错特性来避免局域无规噪声的干扰以实现高精度量子计算。考虑到量子计算所涉及的物理系统大多为多体系统和复合系统，我们选择在绝热量子操控方面具有优越性的超冷原子分子系统作为研究对象。本课题将分别从平均场和全量子角度对超冷玻色原子分子系统的BP开展深入研究，建立量子多体玻色系统BP与经典Hannay角(HA)间的定量关系，揭示量子相变(QPT)和BP间的本质联系，探索通过BP的标度行为对QPT进行分类的标准。另外，本课题还将研究跟BP密切相关的量子干涉问题，通过寻找Stokes相位和HA及BP间的联系探讨利用Ramsey干涉和Landau-Zener-Stuckelberg干涉对BP进实验观测的理论方案。

中文关键词： 绝热几何相位；超冷原子分子；玻色-爱因斯坦凝聚；量子相变；

英文摘要： The Berry phase (BP) is one of the important concepts in quantum mechanics, it is an important part of the quantum adiabatic theory. Recently, BP has shown important applications in quantum information processing and quantum computer design. Quantum information processing employing geometric means to realize high precision quantum computation is mainly taking advantage of the inherent fault-tolerant property of BP to avoid local random noise. The physical systems related to quantum computing are mostly many-body and composite systems. Therefore, we choose the ultracold atomic and molecular systems for BP due to their superiority in adiabatic quantum manipulation. In this proposal, we will study the BP in ultracold bosonic systems from the mean-field and fully quantum perspectives, respectively. We will establish the quantitative relation between the BP and classical Hannay Angle (HA) in quantum many-body systems, reveal the essential connection between quantum phase transition (QPT) and BP, and explore the classification of QPT through the scaling behavior of BP. In addition, in this proposal we will also investigate the quantum interference problems that are closely related to BP. We will study the relation between the Stokes phase and the HA and BP, then we will discuss the theoretical approaches for experimen

英文关键词： adiabatic geometric phase；ultracold atom and molecule；Bose-Einstein condensate；quantum phase transition；