Properties Of Cold Atoms In Artificial Gauge Fields:Anderson Transition And Topological Transition

Using the technology of laser cooling,atoms can be prepared to be near absolute zero,which are called cold atoms.Optical lattices are composed of hundreds of thousands of periodic potential wells formed by the interference of laser beams propagating in the opposite direction.Neutral cold atoms are trapped in the bottom of potential wells,forming the cold atoms in optical lattices.The cold atoms in optical lattices can be used to simulate the electron in the gauge field by introducing the artificial gauge field,resulting in rich quantum phase transitions.Therefore,we take the cold atoms in the artificial gauge fields as the research object and discuss its Anderson localization property and topological property.In Chapter One,firstly,we introduce the composition and characteristics of optical lattices as well as the concept and development of the artificial gauge field.Then,we summarize the development of the Anderson transition and topological transition.Finally,the structure of this thesis is clarified.In Chapter Two,we mainly discuss the Andersen transition of cold atoms.We first propose the concept of non-Abelian self-duality.Our results establish the connection between gauge symmetry and the Andersen transition.By construct-ing the non-Abelian gauge field in the cold atoms,we build the non-Abelian Aubry-Andre-Harper model and discuss the self-dual and generalized self-dual configurations.One is the self-dual configuration,we reveal the phase diagram driven by the non-Abelian gauge field and the existence of the coexistence phase.The other is generalized self-dual configuration,we find that the Anderson tran-sition of cold atoms still satisfies the self-dual transformation mechanism.In Chapter Three,we first summarize the development of topological optical lattices and the quantum spin Hall effect in the cold atoms.Then we introduce the chiral optical ladder and bichromatic optical potential.Next,we discuss the mapping relationship between the spin-orbit coupling,the Zeeman splitting and the chiral ladder.After establishing this mapping,we apply the bichromatic optical potential along the direction of ladder legs,forming the bichromatic chiral ladder.Finally,we reveal the existence of the quantum spin Hall effect and further demonstrate the phase diagram.Our scheme provides a method for realizing the quantum spin Hall effect in cold atoms.In the last chapter,we summarize the Anderson localization property and topological property of cold atoms in artificial gauge fields and give an outlook of the future study in this project..