Quantum Simulation Of Quasi Two-Dimensional ⁸⁷Rb Ultracold Atoms In Optical Lattices

Loading the ultracold atoms in a two-dimensional single layer into the optical lattice results in a pure and easily manipulated two-dimensional system that can well simulate monolayer materials.With the appearance of twisted-bilayer graphene,its excellent properties such as high conductivity,flexibility,and high strength make two-dimensional twisted-bilayer materials become the hottest new materials at present.But the superconducting mechanism of two-dimensional twisted-bilayer graphene is not completely understood,which has become a hot and difficult research topic in condensed matter physics.The aim of this paper is to simulate twisted-bilayer materials by using ultracold atomic systems in twisted-bilayer optical lattices to provide a new method for studying the superconducting mechanism.This thesis involves the following parts:We have realized the preparation of Bose-Einstein condensates.Firstly,87Rb atoms are cooled and trapped by a magneto-optical trap in the first chamber.Then,the atoms are transferred to the second chamber with ultra-high vacuum by means of a series of overlapping coils.In the glass cell,radio-frequency evaporation is carried out in a quadrupole magnetic trap,and then evaporative cooling is completed in a crossed optical dipole trap to obtain 87Rb Bose-Einstein condensates with atomic number of 5×105.In the experiment,absorption imaging is used to detect atoms.A flight time measurement imaging system and a high-resolution in-situ imaging system are constructed.Atomic information in momentum space and real space can be obtained by switching optical paths.An accordion optical lattice with tunable periodicity is used to realize two-dimensional ultracold atoms.A 532 nm laser beam is separated into two parallel beams in the vertical direction.The driving frequency of the acousto-optic deflector can adjust the deflection angle of the 532 nm laser to change the distance between the two laser beams.The two laser beams are then focused on the atoms by an aspherical lens with a focal length of 150 mm,then the two beams interfere to form an accordion lattice with variable periodicity in the vertical direction.The tunable range is 26.7 μm to 3.5 μm.Finally,we got 2.3×105 atoms in a two-dimensional trap with a trapping frequency of 2π× 3.85 kHz.Twisted-bilayer optical lattices are realized based on two-dimensional ultracold atoms.Two square lattices are formed by interfering laser beams at the "tune-out" wavelengths with a small relative angle 5.21°.Two spin states |F=1,mF=1)and |F=2,mF=0)of 87Rb atoms only experience one lattice potential respectively,thus using two spin states to constitute the synthetic dimension to form a bilayer structure.The precisely controllable interlayer coupling is realized by manipulating the microwave to couple the two spin states.The moire pattern in real space is directly observed,which confirms the existence of atomic superfluid in the twisted bilayer lattice.We also find a complex phase transition of superfluid to Mott insulator in the experiment.By using spatial light modulator,two-dimensional atomic arrays with arbitrary shapes are constructed.The weighted Gerchberg-Saxton algorithm is used to generate holograms of various shape arrays.The information of hologram is transformed into optical lattice arrays in real space by using spatial light modulator and lens,then the two-dimensional atomic arrays of arbitrary shapes are realized.In addition,by changing the threedimensional coordinate values of the sites in the phase factor and manipulating the weight factor,the three-dimensional optical lattice arrays and the inhomogeneous optical lattice arrays with controllable intensity can be generated respectively.