Quantum Simulation Of Topological Insulator And Detection Of Its Topological Properties With One-dimensional Optical System

Since the discovery of the quantum Hall effect,the search for new topologi-cal states of quantum materials has been paid much attention in condensed-matter physics.Different from traditional insulators,the topological insulators do not obey the Landau symmetry breaking theory.The topological insulators exhibit as a gap insulating state in the bulk but exhibit as a gapless conducting state at the boundary or surface.These boundary or surface states are protected by topological invariants,so they are immune to the disorders or perturbations.These properties guarantee the potential applications of topological insulators in quantum information pro-cessing and quantum computing.In recent years,it has been found that the one dimensional(1D)topological systems are similar to the high-dimensional topologi-cal insulators that possess rich topological phases,which means that 1D topological systems are significant for revealing and understanding high-dimensional topological systems.Moreover,the flexibility of 1D systems in experiment also make it possi-ble to simulate high-dimensional topological insulators and observe the topological phases.These advantages make the 1D systems become an excellent platform to investigate high-dimensional topological insulators.In this thesis,based on the 1D optical systems,we devote to the simulation of topological insulators and detection of topological proterties,and the main contents are as follows:We realize the simulation of a 1D modulated Rice-Mele model(RMM)and propose a scheme to probe its topological properties with a 1D circuit quantum electrodynamics(QED)lattice.The system can be mapped into a Chern insulator model by introducing a period parameter.We find that the circuit-QED lattice system always exhibits topologically nontrivial phases if both the nearest-neighbor hopping strengthes between two resonators and the qubit-assisted on-site potentials axe periodically changed.The numerical results show that different topological phases can be obtained through modulating the parameter.Furthermore,both the edge state and topological invariant can be unambiguously observed using the cavity field average population and winding number of the reflection coefficient phase.We propose a scheme to simulate a quantum spin Hall insulator caused by the spin orbit coupling with a 1D cavity optomechanical array system.The 1D cavity optomechanical array can be decoupled to two bosonic chains by using diagonaliza-tion method,and each of them can be mapped into the two spin components of the quantum spin Hall insulators.The system can be mapped into a two-dimensional(2D)quantum spin Hall insulator by introducing an additional periodic parameter into present 1D cavity optomechanical array system.The numerical results show that trivial and nontrivial Z2 topological phases can be obtained through modulat-ing the parameter as different values.The analogous spin pumping can be derived with the parameter varying continuously in a period.Besides,the influence of cav-ity decay and resonator damping on the topological properties of the system is also analyzed and discussed.