扩展Jaynes-Cummings-Hubbard模型在一维和三角晶格上的超固体
发布时间：2018-11-03 08:04
【摘要】：本文用平均场方法(MF)和密度矩阵重整化群方法(DMRG)研究了扩展Jaynes-Cummings-Hubbard(JCH)模型,该模型是将多个Jaynes-Cummings(JC)光腔耦合起来,并引入原子之间排斥相互作用得到的。JCH模型可以帮助人们理解光场对量子多体态的调控效应。通过研究我们得到平均场方法下的硬核(光腔中最多可容纳1个光子)、软核(光腔中最多可容纳2个光子)扩展JCH模型的基态相图,并用DMRG方法验证了部分细节图,从而确保相图中的超固体相是稳定存在的。研究发现,对于三角晶格上的硬核扩展JCH模型,有两个激子密度分别为1/3和2/3的固体相。与之前研究的扩展玻色哈伯德模型不同的是,即使光子之间没有排斥相互作用,仍然有光超固体形成。超固体相存在于激子密度分别为1/3和2/3的两个固体相中间,并且在1/3固体相下边缘处也发现了基于空位激发引起的超固体。对于一维硬核和软核扩展JCH模型,我们发现在1/2固体相的下边缘同样存在热力学极限条件下稳定的超固体相。超固体范围内的密度-密度关联对于硬核和软核JCH模型都发现了拍现象。本文的主要内容如下:第一章,介绍了超冷原子的玻色爱因斯坦凝聚、光晶格与光腔晶格、超流相、固体相和超固体相的概念及其应用。并介绍了标准和扩展玻色哈伯德模型、JC模型、JCH模型、扩展JCH模型及其它们的哈密顿量。第二章,介绍了平均场方法,该方法包括:单格点平均场方法和Cluster平均场方法;以及DMRG方法。第三章,分别介绍了用平均场方法和DMRG方法研究的三角晶格上扩展JCH模型以及一维硬核、软核扩展JCH模型的研究结果,并对模拟的结果进行分析。第四章,总结与讨论。
[Abstract]:In this paper, the extended Jaynes-Cummings-Hubbard (JCH) model is studied by means of mean field method (MF) and density matrix renormalization group method (DMRG). The model is coupled with multiple Jaynes-Cummings (JC) optical cavities. The JCH model can help people understand the effect of light field on quantum multi-state. By studying the ground state diagram of the extended JCH model in the mean field method (up to 1 photon in the optical cavity) and soft core (up to 2 photons in the optical cavity), some details of the model are verified by the DMRG method. This ensures that the supersolid phase in the phase diagram is stable. It is found that there are two solid phases with exciton densities of 1 / 3 and 2 / 3 for the extended JCH model on triangular lattice. Unlike the extended Bose Hubbard model previously studied, even if there is no repulsive interaction between photons, there are optical supersolids. The supersolid phase exists between two solid phases with exciton densities of 1 / 3 and 2 / 3, and the supersolids based on vacancy excitation are also found at the bottom edge of 1 / 3 solid phase. For one dimensional hard core and soft core extended JCH model, we find that there are also stable supersolid phases at the lower edge of 1 / 2 solid phase under the thermodynamic limit condition. The density-density correlation in the supersolid range has found beat phenomena for both hard and soft core JCH models. The main contents of this paper are as follows: in Chapter 1, the concepts and applications of Bose-Einstein condensation, optical lattice and cavity lattice, superfluid phase, solid phase and super-solid phase of ultracold atoms are introduced. The standard and extended Bose Hubbard model, JC model, JCH model, extended JCH model and other Hamiltonian quantities are also introduced. In the second chapter, the mean field method is introduced, which includes single lattice mean field method and Cluster mean field method, and DMRG method. In chapter 3, the results of the extended JCH model on triangular lattice and the extended JCH model of one-dimensional hard core and soft core studied by the mean field method and DMRG method are introduced, and the simulation results are analyzed. Chapter IV, summary and discussion.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O469
，
本文编号：2307201
[Abstract]:In this paper, the extended Jaynes-Cummings-Hubbard (JCH) model is studied by means of mean field method (MF) and density matrix renormalization group method (DMRG). The model is coupled with multiple Jaynes-Cummings (JC) optical cavities. The JCH model can help people understand the effect of light field on quantum multi-state. By studying the ground state diagram of the extended JCH model in the mean field method (up to 1 photon in the optical cavity) and soft core (up to 2 photons in the optical cavity), some details of the model are verified by the DMRG method. This ensures that the supersolid phase in the phase diagram is stable. It is found that there are two solid phases with exciton densities of 1 / 3 and 2 / 3 for the extended JCH model on triangular lattice. Unlike the extended Bose Hubbard model previously studied, even if there is no repulsive interaction between photons, there are optical supersolids. The supersolid phase exists between two solid phases with exciton densities of 1 / 3 and 2 / 3, and the supersolids based on vacancy excitation are also found at the bottom edge of 1 / 3 solid phase. For one dimensional hard core and soft core extended JCH model, we find that there are also stable supersolid phases at the lower edge of 1 / 2 solid phase under the thermodynamic limit condition. The density-density correlation in the supersolid range has found beat phenomena for both hard and soft core JCH models. The main contents of this paper are as follows: in Chapter 1, the concepts and applications of Bose-Einstein condensation, optical lattice and cavity lattice, superfluid phase, solid phase and super-solid phase of ultracold atoms are introduced. The standard and extended Bose Hubbard model, JC model, JCH model, extended JCH model and other Hamiltonian quantities are also introduced. In the second chapter, the mean field method is introduced, which includes single lattice mean field method and Cluster mean field method, and DMRG method. In chapter 3, the results of the extended JCH model on triangular lattice and the extended JCH model of one-dimensional hard core and soft core studied by the mean field method and DMRG method are introduced, and the simulation results are analyzed. Chapter IV, summary and discussion.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O469
，
本文编号：2307201
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