Characterizing Topological Phase Of Superlattices In Superconducting Circuits

The idea of using a controllable quantum system to simulate complex quantum matter has been proposed for a long time and has been implemented in supercooled atomic systems.With the development of science and technology,the possibility of quantum simulation is increasing,especially in superconducting circuits.Wider application fields are rapidly expanding,and even relatively simple models have seen more and more new ideas emerging.This paper first reviews the development and research status of quantum simulation,and then discusses in detail the topological properties of the one-dimensional Su-Schrieffer-Heeger model,including energy band structure,topological invariants,etc.Then,we focus on the implementation of this model in superconducting circuits.Based on the recent experimental results of topological magnetons in superconducting qubits,a dimeric quantum qubit chain has been theoretically derived.We further extend this dimeric lattice to superlattices with any number of quantum qubits in each unit cell,which have rich topological properties.In particular,by considering quadrimeric superlattices,we present a dynamic measurement scheme for topological invariants,that is,topological invariants(entanglements)can be characterized by the dynamic correlation of the evolution of a single excited quantum state over time.We demonstrate how to directly measure entanglements through the evolution of initial states over time,and discuss the emergence of corresponding topological protected boundary states.In addition,we also prove that their interference can cause stable Bloch-like-oscillations between multiple interface states.Finally,we discussed the rich topological characteristics of multiband systems,and proposed a theory for measuring the winding number through nonequilibrium dynamics of a single quantum qubit excited state,which is still applicable even in limited sizes.This means that this scheme is easily implemented in experiments,and may provide ideas for the research of topological quantum phase and quantum information processing of topological protection.