【摘要】：本文用平均場方法(MF)和密度矩陣重整化群方法(DMRG)研究了擴展Jaynes-Cummings-Hubbard(JCH)模型,該模型是將多個Jaynes-Cummings(JC)光腔耦合起來,并引入原子之間排斥相互作用得到的。JCH模型可以幫助人們理解光場對量子多體態(tài)的調(diào)控效應(yīng)。通過研究我們得到平均場方法下的硬核(光腔中最多可容納1個光子)、軟核(光腔中最多可容納2個光子)擴展JCH模型的基態(tài)相圖,并用DMRG方法驗證了部分細節(jié)圖,從而確保相圖中的超固體相是穩(wěn)定存在的。研究發(fā)現(xiàn),對于三角晶格上的硬核擴展JCH模型,有兩個激子密度分別為1/3和2/3的固體相。與之前研究的擴展玻色哈伯德模型不同的是,即使光子之間沒有排斥相互作用,仍然有光超固體形成。超固體相存在于激子密度分別為1/3和2/3的兩個固體相中間,并且在1/3固體相下邊緣處也發(fā)現(xiàn)了基于空位激發(fā)引起的超固體。對于一維硬核和軟核擴展JCH模型,我們發(fā)現(xiàn)在1/2固體相的下邊緣同樣存在熱力學(xué)極限條件下穩(wěn)定的超固體相。超固體范圍內(nèi)的密度-密度關(guān)聯(lián)對于硬核和軟核JCH模型都發(fā)現(xiàn)了拍現(xiàn)象。本文的主要內(nèi)容如下:第一章,介紹了超冷原子的玻色愛因斯坦凝聚、光晶格與光腔晶格、超流相、固體相和超固體相的概念及其應(yīng)用。并介紹了標(biāo)準和擴展玻色哈伯德模型、JC模型、JCH模型、擴展JCH模型及其它們的哈密頓量。第二章,介紹了平均場方法,該方法包括:單格點平均場方法和Cluster平均場方法;以及DMRG方法。第三章,分別介紹了用平均場方法和DMRG方法研究的三角晶格上擴展JCH模型以及一維硬核、軟核擴展JCH模型的研究結(jié)果,并對模擬的結(jié)果進行分析。第四章,總結(jié)與討論。
[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.
【學(xué)位授予單位】：太原理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O469
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本文編號：2307201