Experimental Realization Of Two Dimensional Spin-Orbit Coupled Quantum Gas And Uncover Topology With High Precision

Spin-Orbit(SO)coupling is the physical fundamental of a series of novel topo-logical quantum states and topological quantum phases,such as Topological Insulator,Topological Superconductor,Quantum Hall effect,Anomalous Quantum Hall effect,Weyl Semimetal,Majorana Fermions.Topological quantum state is characterized by nonlocal invariants and has rare direct relation to local physical observables.Charac-terizing topological states or phases is often challenging.In solid-state experiments,various characterization strategies have been successfully developed for the discovery of topological insulators and semimetals.Nevertheless,these strategies do not directly measure topological numbers in some circumstances and do not provide explicit evi-dence for topological quantum phases,such as Majorana modes in the topological su-perconductivity.Moreover,in solid materials,such novel quantum topological systems can not usually be realized due to the uncontrollability in growing materials and the impurity of the growth circumstance.The traditional computer simulation of many-particle system come into limitation with the increase of particle number,which leads to the failure of traditional computer simulation.Meanwhile,the appearance and boost-ing development of the technology on ultra-cold atoms provide a possible platform to synthesise such novel topological quantum states and phases,which is often called as quantum simulation.It shows great advantages to solve these quantum ground states directly and provides access to measure the topology directly in these novel topological system.This thesis provides a detail of research on the two-dimensional topology of SO coupled Bose gas,as well as a series of experimental techniques developed in the re-search.Firstly,this thesis will introduce briefly the background,development and ap-plications of the ultra-cold atom techniques,especially the theory of Bose-Einstein Con-densation(BEC)and the application of BEC on the Spin-Orbit coupling.Secondly,this thesis will introduce the already constructed BEC-system.BEC is the experimentally basic object that used as carrier in the works here,which can be produced easily via several ways.The nonnal and frequently used techniques for the BEC production in-cludes:ultra-high vacuum,static electric-magnetic field and its stabilization,lasers and Gaussian beam,non-linear optic,micro-wave and radio frequency,electronics,time se-quence and automation,data processing and coding,laser trapping and cooling.The three experimental systems produce highly pure BEC of 87Rb via forced evaporation in dipole trap and hybrid evaporation,respectively,with the atoms number to be about 2 ×105.Lastly,the thesis introduce in detail the specific works done by the group and the corresponding methods and techniques.The works done includes:1)the first real-ization of two-dimensional(2D)SO coupling in Bse gas.In this work,the ground state of the system can be controlled from ID SO coupling to 2D SO coupling continuously by adjusting the relative phase between two Raman coupling strengths.The topology can be determined by measuring the spin texture in the quasi-momentum space,which indicates that the 2D SO coupled system is topological nontrivial;2)optimization and update of the scheme for realizing 2D SO coupling.The optimized scheme has the advantages of highly C4 symmetry,highly effective Raman coupling,robust and long-lived ground state.The relative phase between two Raman couplings is more easily adj ustable and highly controllable.The magnetic noise is much lower than the previous work,contributing to the long life and high-precision measurement of the 2D SO cou-pling system.By the merit of these advantages,the continuous transition is measured from the stripe phase and plane-wave phase driven by the atoms interaction.Besides,the topological phase diagram is mapped by measuring the spin texture of thermal atoms in low band;3)by quenching the system form topological trivial to nontrivial phase,which is a method of non-equilibrium dynamics,a ring structure of the spin polariza-tion is observed.The ring structure is directly related to the topology of the lowest band,therefore can be applied to determining topology easily and mapping the topo-logical phase diagram precisely;The developed techniques in the research includes the 2D optical lattice,the Kapitza-Dirac diffraction,Raman lattice driven spin-orbit couling and so on.Briefly speaking,quantum simulation with ultra-cold atoms is showing great po-tential and intrinsic advantages in synthesising and researching novel topological quan-tum stats and phases.The 2D SO coupling scheme developed in our group can be con-veniently transferred to other cold-atom system,like 40K fermion system.Our group is now in the process of synthesising higher dimensional SO coupling,stepping forward in exploring abundant novel topological phenomena and other physical phenomena in high-dimension system in the promised future.