一维量子简并气体关联与临界性质研究

项目名称： 一维量子简并气体关联与临界性质研究

项目编号： No.11474189

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： 张云波

作者单位： 山西大学

项目金额： 80万元

中文摘要： 在光晶格中和原子芯片上实现的一维量子简并气体使得可积模型从理论物理学家的案头玩具成为实验上可精确测量、调控的量子多体系统。以Lieb-Lininger 模型为代表的一维可积系统的基态和激发谱可以用Bethe-Ansatz 或其他严格解方法精确得到，但关联函数的计算一直是一个难题，其量子相变过程中的量子临界行为也颇受关注。本项目研究具有丰富内部自由度的一维量子简并原子气体中的关联与临界性质。根据实验上实现的强相互作用的TG 气体和一维强相互作用费米气体等进展，利用密度泛函理论、密度矩阵重整化群和非线性Luttinger 液体理论研究非均匀系统中时间、空间及自旋关联函数的计算，关联量子态的相干传播和量子颤振现象，以及量子临界行为的标度及相变边界的确定等问题。关联和临界性质的研究对实验上设计超高空间分辨率的原位测量系统和建立准确描述新型关联量子系统理论模型具有重要的意义。

中文关键词： 冷原子物理；超冷原子气体；量子相变；玻色爱因斯坦凝聚

英文摘要： The realization of one-dimensional(1D) quantum degenerate gas in optical lattices or atom chips allows a parameter-free comparison of theoretical predictions with measurement for a class of exactly solvable or integrable models. The energy spectra and thermodynamical properties can be calculated exactly using Bethe ansatz. The calculation of correlation functions, however, is a much more complicated task. On the other hand, 1D quantum critical phenomena provide an insight into the thermodynamical properties in quantum critical regimes. We investigate the correltation and criticality of 1D quantum degenerate gas with rich internal degrees of freedom. Specifically, following the recent progress in realization of Tonks-Girardeau gas and 1D strongly interacting Fermi gas, we apply the Density Functional Theory, Density Matrix Renormalization Group, Time-Evolving Block Decimation Algorithm, and the nonlinear Luttinger liquid theory to 1D quantum degenerate gas, in order to improve the calculation of space, time and spin correlation function, to study the propagation of correlated quantum states and quantum flutter phenomena, to obtain the universal scaling law of the quantumcritical behaviour, and to determine the phase boundary of various quantum phases at finite temperature. These properties are essential to the design of the single-atom-resolved in-situ imaging system and to the establishment of theoretical model for the novel correlated systems.

英文关键词： Cold Atom Physics;Ultracold Atomic Gas;Quantum Phase Transition;Bose-Einstein Condensation