摘要
随着实验技术的不断发展,玻色-爱因斯坦凝聚这一物理现象在许多国家的实验室中都得以实现。这不仅证明了爱因斯坦的预言,也为我们研究原子的低温动力学性质,以及认识其他的低温物理现象提供了一种新的途径。
对于一个量子系统,涨落将引起系统的相变,而对于低温情况,系统的热涨落将不再存在,但是根据海森堡不确定关系,量子涨落却依然存在,如果这个涨落足够大,就会引起相变。超流-Mott绝缘相变就是由这样的量子涨落所引起。将超冷玻色子装载到光晶格中,原子会在晶格之间发生移动,即隧穿,就形成超流,当原子与原子的相互作用能比隧穿小便形成超流,通过增加势垒的高度,可以得到更大的束缚能,即可以实现超流相向Mott绝缘相的转变。
本文主要研究的是光晶格中自旋为3的玻色子系统的超流-Mott绝缘相变问题。我们从系统的Bose-Hubbard哈密顿量出发,通过构建多粒子对称态来描述系统的本征态,并且用二阶微扰理论计算了微扰矩阵元对基态能量进行修正,得到超流-Mott绝缘相变条件以及相图。从而我们得到系统实现超流-Mott绝缘相变的边界,以及超流组分随着自旋磁量子数的不同而分离的规律,并且总结参数的变化对超流区域的影响,为实验上探测超流以及超流组分分离提供了理论指导。
本文包括以下四个部分。首先,第一部分主要简单介绍玻色一爱因斯坦凝聚的基本物理性质以及与其相关方面研究的新进展,包括实验上的实现等。第二部分主要是介绍几种常见的光晶格以及玻色—哈伯特(Hubbard)模型,并且简单介绍了自旋为1、2的玻色系统。第三部分研究光晶格中自旋3的超冷玻色系统的超流—Mott绝缘相变,包括理论模型的建立、本征态和能量本征值的计算以及通过微扰计算得到的相图,最后对得到的相图进行分析,讨论相变的性质和规律。最后一部分对本文做简要总结以及对该领域前景的展望。
With the rapid development of experimental technique, the physical phenomena, Bose-Einstein condensation (BEC), has been realized in laboratories of several countries, which has not only testified Einstein's prophesy, but also has provided us with a new method to study the nature of low temperature dynamics of atoms and to know other low temperature physical phenomena.
The fluctuating of a quantum system will cause the transition of it, but when the system is in a low temperature, the thermal fluctuating will no longer exist. However, according to Heisenberg's uncertainty relationship, the quantum fluctuating does exist, and as long as it is high enough, it will cause the transition of the quantum system, and a typical example is Superfiuity-Mott insulator (SF-MI) transition. Put ultracold bosons into optical lattices, and atoms will move among the optical lattices, which is called tunneling, and then superfluity is formed. When mutual action between atoms is smaller than that of tunneling, superfluity will be formed, and by raising the height of potential barrier, larger structure energy will be got, that is, the transition of Superfluity-Mott insulator will be realized.
The thesis, mainly, studies Superfluity-Mott insulator (SF-MI) transition of ultracold spin-3 bosons in an optical lattice. Starting from Bose-Hubbard model of the system, we construct many-body symmetry states to describe eigenstates of the system and calculate matrix elements through the theory of second order perturbation, which modifies the ground state energy and gets the conditions of the transition of Superfluity-Mott and its phase diagrams. And therefore we get the boundaries that the system can realize Superfluity-Mott insulator (SF-MI) transition, and we also discover the rules that superfluity separates with different magnetic number of spin. In addition, we summarize the effect of the change of parameter towards superfluity area, which provides a theoretical instruction for detecting superfluity and superfluity component separation experimentally.
The thesis is consisted of four parts. The first part is a brief introduction of the basic nature of Bose-Einstein condensation and the new development of its relevant research, including the realization of experiment and so on. The second part is an introduction of some familiar optical lattices and the recent development of Superfluity-Mott transition and Bose-Hubbard mold, including Bose systems of spin-2 and spin-3. The third part is an introduction of Superfluity-Mott transition of ultracold spin-3 bosons in an optical lattice, including the establishment of theory model, eigenstates, and the calculation of energy eigenvalues, as well as phase diagrams gained from perturbation theory. Finally, the phase diagrams are analyzed and the nature and rule are discussed. The last part of the thesis is a brief summary, and also shows the expectation of the future of this field.
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