非均匀光晶格中超冷原子的量子相变

发布时间：2018-04-11 00:01

本文选题：玻色-爱因斯坦凝聚 + Feshbach共振　；参考：《东南大学》2017年硕士论文

【摘要】：自从玻色-爱因斯坦凝聚实现以来,超冷原子物理成为了热门的研究领域之一。超冷原子体系是凝聚态物理和原子物理中研究的一项重要课题,它将用于原子干涉仪、冷原子钟、量子计算机的开发以及实现。继在光晶格中预言并且观测到超冷原子的超流-莫特绝缘体相变之后,人们对光晶格中超冷原子系统中潜在的量子相做了大量的研究。本文基于扩展的玻色-哈伯德模型,对非均匀光晶格中超冷玻色原子体系的基态做了研究,其中光晶格的非均匀性主要体现在以下两个方面:一是额外施加一个谐振势;二是认为光晶格不同格点上原子之间存在不同的相互作用。依据平均场近似以及数值对角化方法,计算了表征体系基态性质的一些参数,即平均粒子数以及序参量,结果表明在合适的参数下非均匀的光晶格中同时存在莫特绝缘相和超流相。全文共分五章,具体如下:第一章首先介绍了玻色-爱因斯坦凝聚的概念以及发展,然后详细回顾了原子冷却与囚禁技术和Feshbach共振技术,最后简要概述了玻色-爱因斯坦凝聚的理论基础,即平均场理论和Gross-Pitaevskii方程。第二章描述了光晶格,量子相变的概念以及用来研究光晶格中超冷原子发生相变的模型。第三章研究了在外加谐振势的二维正方光晶格中超冷原子系统的量子相变,首先推导出此体系的哈密顿量,进一步通过平均场理论分离出单个格点的哈密顿量,最后用数值对角化方法得到系统的基态,并分析相图以及平均粒子数三维图得出结论:莫特绝缘相与超流相共存于非均匀的光晶格中。第四章研究了在二维正方光晶格中存在非均匀的排斥相互作用的超冷原子系统的量子相变,运用与第三章类似的方法,采用平均场近似方法分离出单个格点的哈密顿量并用数值对角化方法得到系统的基态,最后分析相图以及平均粒子数三维图得出结论:莫特绝缘相与超流相共存于光晶格中。第五章对全文进行了总结和展望。
[Abstract]:Since the realization of Bose-Einstein condensation, ultracold atomic physics has become one of the hot research fields.Ultracold atomic system is an important subject in condensed matter physics and atomic physics. It will be used in the development and implementation of atomic interferometer, cold atomic clock and quantum computer.Following the prediction and observation of superfluid-Mott insulator phase transitions of ultra-cold atoms in optical lattices, a great deal of research has been done on the potential quantum phases in ultralow atomic systems in optical lattices.Based on the extended Bose-Hubbard model, the ground state of the supercooled boson atom system in the inhomogeneous optical lattice is studied in this paper. The inhomogeneity of the optical lattice is mainly reflected in the following two aspects: first, an extra resonant potential is applied;The second is that there are different interactions between atoms at different lattice points in the optical lattice.Based on the mean field approximation and the numerical diagonalization method, some parameters representing the properties of the ground state of the system, namely, the average number of particles and the order parameters, are calculated.The results show that both Mott insulating phase and supercurrent phase exist in the non-uniform optical lattice under suitable parameters.In chapter 1, the concept and development of Bose-Einstein condensation are introduced, and then atomic cooling and trapping techniques and Feshbach resonance techniques are reviewed in detail.Finally, the theoretical basis of Bose-Einstein condensation, namely, mean field theory and Gross-Pitaevskii equation, is briefly summarized.In chapter 2, the concepts of optical lattice, quantum phase transition and the model used to study the phase transition of supercooled atoms in optical lattice are described.In chapter 3, the quantum phase transition of ultracold atomic system in two-dimensional square optical lattice with external resonance potential is studied. Firstly, the Hamiltonian of the system is derived, and the Hamiltonian of a single lattice is further separated by the mean field theory.Finally, the ground state of the system is obtained by numerical diagonalization, and the phase diagram and the three dimensional average particle number diagram are analyzed. It is concluded that the Mott insulated phase and the supercurrent phase coexist in the non-uniform optical lattice.In chapter 4, the quantum phase transition of ultracold atomic system with inhomogeneous repulsive interaction in two-dimensional square optical lattice is studied.The Hamiltonian of a single lattice point is separated by the mean field approximation method and the ground state of the system is obtained by numerical diagonalization. Finally, the phase diagram and the three dimensional figure of the average particle number are analyzed. It is concluded that the Mott insulated phase and the supercurrent phase coexist in the optical lattice.The fifth chapter summarizes and prospects the full text.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O469

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