Topological Quantum Simulation Based On Cold Atoms In The Momentum Space

In recent years,the regulation techniques of quantum systems have become more and more mature.Compared with the traditional experiment of condensed matter physics,the system itself has better controllability.On the other hand,since the Bose Einstein condensate was born in 1995,more and more experimental groups have devoted themselves to the field of ultra-cold atoms,and the manipulation techniques of ultra-cold atomic systems have become more and more mature and diversified.Since the quantum Hall effect was discovered in the 1980s,topology has gradually entered physics.The direction of topological quantum simulation has been gradually developed.Many groups have carried out research on topological quantum simulation using the ultra-cold atom platform.In this paper,we report that we have built an experimental setup for 87RbBose Einstein condensates,which uses a 2D magneto-optical trap(MOT)technique to accelerate the collection of atoms in high vacuum cavity.Using a 3D magneto-optical trap,the atoms coming through the low vacuum chamber are collected and cooled.It is then loaded into an optical trap,where the atoms are cooled by polarization gradients,followed by evaporative cooling to produce the rubidium Bose Einstein condensate(BEC).On the basis of the BEC device,a laser generating a one-dimensional momentum lattice is added.Two topological quantum simulations are carried out on the basis of one-dimensional momentum space lattices.The first work is the study of the related topological properties of extended SSH model-SSH4.The authors implement the SSH4 model in the momentum space lattice by using ultra-cold atoms.It is verified by experiments that the model’s winding number can be obtained by the higher dimensional extension of the mean chiral displacement.The topological phase transition of the system is given experimentally,and the topological edge states are confirmed by quenching dynamics.The second work is the study of the topological properties of discrete time quantum walk.The topological quantum walk in discrete time is realized by using the ultra-cold atom in the momentum space lattice.The topological properties of the system are proved experimentally by measuring the time average chiral displacement and the second order statistical moment.In addition,the interaction induced localization in quantum walk dynamics is also observed experimentally.Finally,we put forward some suggestions to improve the errors of the system,in order to further improve the accuracy of the experiment and carry out research on topological quantum simulation with higher complexity.