光晶格中的超冷原子一直是凝聚态领域关注的重点问题，由于光晶格的纯净性和可操控性，人们常用光晶格系统来模拟固体晶格中的问题，并由此验证并发现了许多新奇的量子现象，如超布洛赫振荡等。而自旋轨道耦合效应是近几年非常具有生命力的课题，随着人们对于自旋电子学的研究不断深入，越来越多的新奇与重要的物理现象相继被发现，如：量子自旋霍尔效应，自旋量子计算和拓扑绝缘体的发现都和自旋-轨道耦合有着密切的联系。本文主要研究自旋轨道耦合粒子在光晶格中的拓扑相变和布洛赫振荡问题。 第一章是绪论，我们简要介绍了光晶格、哈伯德模型及自旋轨道耦合及布洛赫振荡的历史背景和研究现状，并从实验和理论两方面阐述了实现自旋轨道耦合的方法，给出了我们研究问题所采用的模型：具有自旋轨道耦合作用的一维两组分哈伯德模型。 第二章我们讨论了含有自旋轨道耦合作用的一维光晶格系统的拓扑相变的问题。主要研究了两种不同的自旋轨道耦合方式：k_x σ_y和k_x σ_y+k_x σ_z下体系的拓扑性。发现通常形式自旋轨道耦合k_x σ_y（或k_x σ_x）不能够使体系产生拓扑性。但是当加入推广的自旋轨道耦合作用k_x (σ_y+σ_z)时，体系存在拓扑相，并且可以通过操控自旋空间的旋转角度和自旋轨道耦合强度来使体系发生拓扑—非拓扑的相变。我们找到了相变条件，并且通过验证边界态的存在证实了相变条件。 第三章我们在第二章所构建的推广形式的自旋轨道耦合系统下，通过加入恒定外场力来使波包在光晶格中做布洛赫振荡。发现在该模型下存在着手性布洛赫振荡。并且在拓扑相变点，布洛赫振荡的周期与粒子自旋极化周期存在二倍关系，并且探讨了产生这一关系的物理机制。 最后是全文的总结并对该课题的前景做进一步的展望。

Ultracold atom in the optical lattice have always been the focus of attention in the condensed matter physics. Due to the purity and controllability of the optical lattice, people often use the optical lattice system to simulate the solid crystal lattice, and thus verify and discover many novel quantum phenomena, such as Super Bloch Oscillations. The spin-orbit coupling effect is a hot topic in the condensed matter physics in recent years. In recent years, people have continued to deepen their research on Spintronics, and more and more novel and important physical phenomena have been discovered, such as Quantum spin hall effect, Spin quantum calculation, and the discovery of topological insulators are all closely related to spin-orbit coupling. This paper mainly studies the topological phase transitions and Bloch oscillations of spin-orbit coupled particles in optical lattices. For the first part, we briefly introduce the historical background and research status of the optical lattice, Hubbard model, spin-orbit coupling and Bloch oscillation, and elaborate the realization of spin-orbit coupling from both experimental and theoretical aspects. The method gives a model for our research problem: One-dimensional two-component Hubbard model with spin-orbit coupling. For the second part, we discuss the problem of the topological phase transition of a one-dimensional optical lattice system with spin-orbit coupling. Two different methods of spin-orbit coupling are studied: the topology of k_x σ_y and k_x σ_y+k_x σ_z. It is found that the general form of spin-orbit couplingk_x σ_y (or k_x σ_x) can not make the system topology. However, when the generalized spin-orbit coupling function k_x σ_y+k_x σ_z is added, the system has a topological phase, and the topological-trivial phase transition of the system can be achieved by manipulating the free space rotation angle and spin-orbit coupling strength. We found the phase transition conditions and verified the phase transition conditions by verifying the existence of the boundary states. For the third part, we use the extended spin-orbit coupling system constructed in part second to make the Bloch oscillation in the optical lattice by adding a constant external field force. It is found that Chiral Bloch oscillation exists in this model. And at the topological phase transition point, there is a double relationship between the cycle of Bloch oscillation and the cycle of particle spin polarization, and the physical explanation for this relationship is discussed. Finally, it is the summary of the full text and further prospects for the future of this topic.