Simulation And Investigation Of Topological Physics In Cold Atoms And Synthetic System Of Photons

In recent years,topological physics has attracted people's attention in many zones.In 1980,quantum Hall effect was discovered,subjected in strong magnetic fields and low temperatures.Hall conductance undergoes quantum Hall transitions to take on the quantized values.After that,more quantized effects have been found,such as quantum anomalous Hall effect,quantum spin Hall effect,fractional quantum Hall effect and etc.Those effects have a mathematical correspondence,called topological number,which cannot be modified by a smooth fluctuation or impurity without breaking the gap.In 1982,Thouless,Kohmoto,Nightingale and den Nijs raise a topological number,called TKNN number,in magnetic Brillouin zone,which can be used to explain the quantum Hall effect After that,more topological numbers have been found in various dimension and symmetry,such as winding number and Zak phase,which also has its own physics corresponds.Another topological effects are the topological protected edge states,which appear on the boundary of the topological non-trivial materials and topological trivial materials,such as Majorana Fermion,Dirac Fermion,surface Fermi arcs.Because the energy gap protects the topology of the phase,which is broken on the boundary,the gapless edge states appear.These states are also an essential property of the topological effects,which almost explain all the quantized effects,such as quantum Hall effect.The gapless edge states attribute to Hall conductance,as the states can be excited by the electric fields.As the edge states are protected by topology and the number of the edge states equal the difference of the topological invariants,the Hall conductance is quantized.The topological non-trivial model is also realized in other platforms,such as cold atoms,photonic resonant cavities and etc.Those platforms have its own property.For example,we can use the Feshbach resonance to control the interactions between atoms,use optical lattices to realize lattice model in cold atoms,and use Raman laser induced hopping to realize spin-orbit couplings and synthetic magnetic fields in the system.In resonant cavities system,the linear optical devices can modify the strength and phase of the laser.In our research,we focus on the topological property in those platforms.We study the effects of synthetic spin-orbit coupling on the pairing physics in an ultracold quasi-one-dimensional alkaline-earth-like atoms near an orbital Feshbach res-onance(OFR).The interplay between spin-orbit coupling and pairing interactions near the OFR leads to an interesting topological Fulde-Ferrell state,where the non-trivial topology of the state is solely encoded in the closed channel with a topologically triv-ial Fulde-Ferrell pairing in the open channel.We confirm the topological property of the system by characterizing the Zak phase and the edge states.The topological Fulde-Ferrell state can be identified by the momentum-space density distribution obtained from time-of-flight images.On the other hand,we study the topological effects of the degenerate resonant cav-ities.Previously,people raise the methods using the orbit angular momentum(OAM)degrees of light to simulate one dimension degrees of a lattice model,including to realize two(one)dimensional lattice using one dimension cavities(one cavity),re-spectively.Moreover,these works allow us to ask a question:is it possible to construct all kinds of lattice models in currently experimentally available systems?We create a scheme to realize all kinds of lattice models using one degenerate resonant cavity.In this scheme,we use one-dimensional OAM degrees of freedom to realize all internal and exterior degrees of freedom of a lattice model.Then we couple any kinds of optical OAM modes with the aid of spatial light modulators(SLMs).The hopping amplitudes depending on the internal degrees of freedom can be realized by the beam rotators in-ducing OAM dependent hopping phases.In these basis,we show an example to realize a four dimensional time-reversered invariant topological non-trivial models,and use Chem number and chirality of edge states to confirm the topology of the model.In this work,we create a ideal platform to realize all kinds of lattice model.