Experimental Study On Non-equilibrium Dynamics Of Spin-Orbit Coupled Quantum Gas

Since the discovery of a novel and fundamental phase of matter——topological phase in the 1980s,topological quantum matter has intense interest due to peculiar physical properties and broad potential applications.Several topological systems have been constructed in the ultracold atom communnity,but there are always various difficulties in measuring the topological properties of the system.This thesis mainly discusses how to use non-equilibrium dynamics on the ultracold atomic experimental platform to study topological properties of the spin-orbit(SO)coupled artifical gauge field and construct new topological structures.This thesis in the first three chapters firstly introduces some background knowledge involving non-equilibrium dynamics and spin-orbit coupled gauge field in the ultracold atomic system.In the introduction,I berifly describe the research status of noneuquilibrium dynamics and spin-orbit coupling effect.Chapter 2 introduces the theoretical scheme synthetized one-dimensional(1D)and two-dimensional(2D)spin-orbit coupled gauge field and related properties.Chapter 3 introduces some related technologies,including the expertimental protocol realizing Bose-Einstein condensates(BEC),artifical synthetic 2D SO coupling gauge field and its parameters calibration.And then,my mainly research achievement is introduced detailedly from Chapter 4 to Chapter 6.Chapter 4 elaborates the obtainment of complete topological information of the equbilbrium system by quench dynamics.Here,We have devopled a set of technologies that can measure all Bloch vectors equivalently:(1)Quenching all quantum axes of 2D SO coupled Hamiltonian and only measuring the time evolution of only one Bloch vector for each quench;(2)Calculating time average of this Bloch vector.Thus,all the topologial charges and band-inversion surfaces are observed by spin textures from time-average of Bloch vectors.The Chern number of the post-quench Hamiltonian is determined by the total topological charges in the region enclosed by band-inversion surfaces.Further,the dynamical field defined on the band-inversion surfaces is also used to extract the Chern number of post-quench Hamiltonian,and renders the dynamical bulk-surface correspondence.Chapter 5 elaborates how to contruct a novel topological structure by quench dynamics,and proposes a theoretical scheme to measure all Bloch vectors.According to Hopf map,a two dimensional momentum plus one-dimensional time(2+1)dynamical Hopf insulator is synthsized by quench a quantum axis of 2D SO coupling.By observing Hopf links and Hopf fibration,the synthesis of dynamical Hopf insulator is proved.The South and North on the Bloch sphere form two Hopf fibers in the(2+1)D space,that is,Hopf links.The other latitude circles on the Bloch sphere form Hopf tori in the(2+1)D space.Hopf tori consist of Hopf fibers,thus also called Hopf fibration.However,we do not observe all Hopf fibers if only a Bloch vector is measured.To this end,we further propose the theoretical scheme of the tomography of Bloch vectors-Raman pulse method,which can extract the complete topological information of the system.Chapter 6 elaborates exploring Kibble-Zurek mechanism in a 1D spin-orbit coupled system.We ramp down the Raman coupling strength with finite rate from the high symmetry phase to low symmetry phase,and then use spin-resolved time-of-flight(TOF)to observe the momentum distribution of atomic cloud which emerges delayed bifurcation structures and the fragement information.The universal power law scalings of spatiotemporal dynamics are obtained by the fluctuations of momentum distribution and fragements,which is consistent with scalings predicted by homogeneous and inhomogeneous Kibble-Zurek mechanism.In summary,Non-equilibrium dynamics have potential applications in detecting topology of equilibrium state,synthesizing novel topological phase and studying dynamic quantum phase transition.Especially,dynamical classification of topological phases in the future is expected to become a general technology for studying topological properties of cold atom system.