Study On Quantum Simulation Of One-dimension Topologic System Based On Coupled-cavity Array

Topological insulators are new states of quantum matter which cannot be simply connected to conventional insulators and semiconductors.They are new electronic materials that have a bulk band gap like an ordinary insulator but have protected and gapless conducting states on their edge or surface.These states are possible due to the combination of spin-orbit interactions and time-reversal sym-metry.Moreover,there is a direct analogy between superconductors and insulators because the Bogoliubov-de Gennes Hamiltonian for the quasiparticles of a super-conductor is analogous to the Hamiltonian of a band insulator,with the supercon-ducting gap corresponding to the band gap of the insulator.Hence,topological superconductors emerge.Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions,and provide a new venue and approach for realizing proposals for topological quantum computation.These topological materials have been theoretically predicted and experimentally observed in a variety of systems.In this thesis,we devote to the simulation and study of one-dimension typical topological insulator and superconductor,and the main contents are as follows:Based on the coupled-cavity array,we study the effects of the position of the pas-sive and active cavities on the spontaneous parity-time-(PT)symmetry-breaking behavior in a non-Hermitian coupled-cavity-array.We analyze and discuss the en-ergy spectra and PT symmetry in the topologically trivial and nontrivial regimes under three different cases in detail;that is,the passive and active cavities are located at,respectively,the two end positions,the second and penultimate posi-tions,and each position in the coupled-cavity array.The odevity of the number of cavities is further considered to check the effects of the non-Hermitian terms ap-plied on the PT-symmetric and-asymmetric systems.We find that the position of the passive and active cavities has remarkable impacts on the spontaneous PT-symmetry-breaking behavior,and in each case the system exhibits distinguishable and novel spontaneous PT-symmetry-breaking characteristics.The effects of the non-Hermitian terms on the PT-symmetric and-asymmetric systems due to the odevity are comparatively different in the first case but qualitatively the same in the second case.Based on the charged whispering-gallery microcavity array,we simulate the nor-mal Kitaev model and find that the system reveals profound connections with the normal Kitaev model and its some derivatives.Furthermore,the topological prop-erty of the system depends on effective optomechanical coupling strength deeply.In the optomechanically induced Kitaev topologically nontrivial phase,compared to the normal Kitaev model in the Majorana basis,the novel and distinct struc-ture of charged whispering-gallery microcavity array leads to controllable photonic and phononic edge localization.As an example,furthermore,we also simulate the extended Kitaev model and show that two topologically different nontrivial phases the system holds allow one to realize more freewheeling controllable photonic and phononic edge localization.The system offers an alternative approach to correlate with other more complicated one-dimensional noninteracting spinless topological models relevant to the p-wave superconducting pairing.