Topological Nodal Chains In Ultracold Atom System

With the successful development of the world's first laser in 1960,the laser known as the "the fastest knife","the most accurate ruler" and "the brightest light" began its use in various fields of scientific research and social life.The application has greatly promoted the development of science,technology and the progress of society.By applying it to the micro world,people can also understand the essence and mystery of the macro world more accurately.At the end of the 20 th century,Steven Chu and others won the Nobel Prize in Physics for their pioneering research in the field of ultracold atoms.Since then,the ultracold atom system,as a human-controlled platform,has been active in many cutting-edge studies of physics,and the interaction between light and atoms has also been widely used in all walks of life.In particular,the recently proposed optical Raman lattice scheme can be used to design various types of high dimensional spin orbit coupling,and it shows high controllability.The realized spin orbit coupling quantum gas has the characteristics of long life.With these research advances,the construction of high-dimensional spin-orbit coupling has developed into a very important research direction.Since the 2016 Nobel Prize in Physics was awarded to scientists who are engaged in the study of topological phase transitions and topological phase theories of matter,topology has set off a wave in the field of physics.A series of novel topological phenomena and topological states of matter were discovered by researchers.Due to the complex structure and interaction within natural solid materials,the detection of novel topological states is relatively limited.Afterwards,the combination of the advantages of the ultracold atomic system and the topological states of matter has formed the research field of artificial topological state in the ultracold atomic system.In just a few years,the research in this field has shifted from topological insulators to semimetals,and Weyl semimetals have also been realized and detected recently.Therefore,in this thesis,we turn our attention to another class of semimetals with more rich properties,namely topological nodal line semimetals.Topological nodal rings as the simplest topological nodal lines recently have been extensively studied in optical lattices.However,the realization of complex nodal line structures like nodal chains in this system remains a crucial challenge.Here,this thesis proposes an experimental scheme to realize and detect topological nodal chains in optical Raman lattices.Specifically,the thesis construct a three-dimensional optical Raman lattice which supports next nearest-neighbor spin-orbit couplings and hosts topological nodal chains in its energy spectra.Interestingly,the realized nodal chains are protected by mirror symmetry and could be tuned into a large variety of shapes,including the inner and outer nodal chains.In addition,this thesis also demonstrates that the shapes of the nodal chains could be detected by measuring spin polarizations.The research of this thesis opens up the possibility of exploring topological nodal chain semimetal phases in optical lattices.