Simulating And Studying The Topological Properties Of Commensurate Aubry-Andr(?)-Harper Model With Microresonator Array

In recent years,the discovery of topological insulator has became a hot research direction in condensed matter physics.The topological insulator is a completely new type of insulator,energy gap exists in topological insulator the same as general insulator,but only the edge states exist in topological insulator,which is a novel character with respect to topological insulator.We could calculate the value of topological invariant to investigate the systematic topological property.Due to that the novel character has attracted extensive attention,and some achievements have been achieved in theoretical and experimental areas.Meanwhile,we find that topological properties exist not only in the electronic system,analogously,we can simulate the topological system with photonic,which has become a new research field.The Aubry-Andre or Harper(AAH)model has been the subject of extensive theoretical research in thecontext of quantum localization.Recently,it was shown that one-dimensional quasicrystals described by the nontrivial topological incom-mensurate AAH model.We propose a scheme for simulating and studying the topological properties of generalized commensurate AAH model with whispering-gallery-mode(WGM)microtoroid microresonator array.In our scheme,we trap a atom on each WGM resonator,and the next-nearest-neighbor hopping can be mod-ulated by waveguides.As a result,the generalized commensurate AAH model is simulated successfully by choosing the feasible parameters experimentally,and we obtain the rich phase diagrams,the edge state exist in off-diagonal AAH model.We discuss two cases of two energy band and three energy band.Finally,we also discuss the possibility of experimental implementation,which shows that our scheme can be effectively implemented under the current technology.