Microscopy Of Quantum Criticality And Spin Models Of Low-Dimensional Systems In Optical Lattices

Ultracold atoms in optical lattices is one of the promising platforms for large-scale quantum simulation and quantum computation,which features long coherence time,versatile controllability and easy scalability.In this thesis we focus on the quantum Simulation of several low-dimensional models including one-dimensional Tomonaga-Luttinger liquids and Heisenberg models with ultracold rubidium atoms in optical lattices.One-dimensional hard-core bosons manifests universality in quantum critical region.We prepared one-dimensional degenerate Bose gas and verified these universal scaling behaviors in ultracold atoms experiments,benefiting from the high-resolution absorption imaging.The results shown that critical exponents were z=2.3-0.3+0.6,v=0.56-0.08+0.07.The measured Luttinger parameters and the power law decay of the density profiles in momentum space suggested the existence of Tomonaga-Luttinger liquids.We built a quantum gas microscope with single-site and single-atom resolution.A Bose-Einstein condensate of 87Rb atoms was sliced to multilayers by optical lattices and only a single layer was selected.Afterwards,the selected atoms were loaded to optical lattices with spacing of 532 nm,interfered by retro-reflected 1064 nm lasers.Pinned with the same lattices,atoms were site-resolved from the microscope by 780 nm fluorescence imaging whose full-width-half-maximum resolution was calibrated to 576 nm.We observed the superfluid to Mott insulator transition after further evaporative cooling the atoms in two-dimensional system.The shell structure of the Mott insulator was captured from the microscope.The particle number statistics on sites varied with lattice depth,indicating a temperature lower than 0.15 U。To eliminate the inhomogeneity associated with the lattice beams,an anti-gaussian potential was projected from a digital micro-mirror device through the objective.We updated single-color lattices to spin-dependent bichromatic superlattices in X,Y directions for the quantum gas microscope.Long lattices were made from 1064 nm lasers and short lattices from 532 nm ones,whose lattice constants were 1260 nm and 630 nm respectively.Long lattices equipped with electro optical modulators and short lattices formed spin-dependent superlattices,which enabled us to parallelly address the spins site-resolved in double wells.To resolve superlattice sites the atoms were pinned in the short lattices with high power 532 nm lasers.Similar to the single-color lattice case,atoms were cooled to condensation in the selected layer.The superfluid to Mott insulator phase transition was observed in short lattices.The Mott insulator was prepared to half-filling.The phase of superlattices were calibrated to balanced by rotating the phase plates inserted in optics paths of long lattices.We demonstrated the spindependent effect on |↑>=|F=2,mF=-2)and |↓>=|F=1,mF=-1>states by rotating the polarization of one long lattice.After initialization to a Neel order,time-and site-resolved single particle tunnelling and spin superexchange dynamics were observed under the quantum gas microscope.The Neel order was achieved by addressing spins in left or right sites of double wells,whose fidelity was 95%.The tunnelling rate was J～h×110 Hz and the superexchange Jex=h×31(1)Hz which agreed with predictions.These abilities of single-atom and single-site manipulation and detection will pave the way to quantum simulation of spin models and interacting topological models in low dimensions,as well as to preparation of large-scale entanglement states.