Study On Two-dimensional Spin-orbit Coupling Bose Gas And Its Related Experimental Techniques

This thesis is a summary of the author's study and work during the Ph.D.It mainly focuses on the simulation and the research of superfluid,topological insulator and some other physical problems,which are all based on Spin-Orbit Coupling(SOC)on an ultra-cold atomic platform.In the course of the research,we explored different properties of the SOC system and developed some technical methods as needed.In this thesis,I first briefly describe the basic theory of Bose-Einstein Conden-sate(BEC)and the properties of SOC,and introduce the theoretical and experimental schemes for constructing SOC.Then I describe the experimental setups.Later,a se-ries of experimental studies on one-dimensional/two-dimensional SOC are introduced.First,we use the Bragg spectroscopy to get the excitation spectrum of one-dimensional SOC BEC,and found the roton-type structure in the magnetized phase.The adjustment of phonon mode and roton mode can be realized by changing the coupling strength or double photon detuning.It is the first time in the experiment to observe the roton mode in the weak and short-range interaction system,which provides a new idea for the simulation of strong correlation system in the future.Second,we propose a simple scheme to realize a two-dimensional SOC and successfully achieve it experimentally.The scheme is simple and easy,and does not require complicated techniques such as precision phase locking and fine adjustment of light potential.The constructed sys-tem has the characteristics of adjustable dimensions,small heating and stable topology.In the two-dimensional SOC system,we observe the ground state of the system in the momentum space,the evolution of the two-dimensional to one-dimensional SOC and the topological phase transition of the system.Based on the existing two-dimensional SOC scheme,we upgrade the scheme to make the system with a complete C4 symme-try,Then we upgrade the vacuum system and improve the bias magnetic field system to make the experimental setup more simple and stable,and the life time of the system has also been greatly improved.In the new two-dimensional SOC system,we study the continuous evolution of the system from two-dimensional to one-dimensional to two-dimensional,the life time of the system,the interaction phase diagram,the topological phase diagram,the topological band structures of the system.Finally,we upgrade and optimize the bias magnetic field system.The noise of the bias magnetic field has been greatly reduced,the bias magnetic field has been stabilized,and the long-term instabil-ity of the system has been decreased.It is prepared for the three-dimensional or even higher dimensional SOC experiments or some other higher precision experiments in the future.