Since the 1990s,femtosecond laser two-photon absorption(TPA),which enables point-by-point photopolymerization,has been a tool for making threedimensional(3D)microstructures.Approximately 10 years later,Kawata et al.im...Since the 1990s,femtosecond laser two-photon absorption(TPA),which enables point-by-point photopolymerization,has been a tool for making threedimensional(3D)microstructures.Approximately 10 years later,Kawata et al.improved the spatial resolution of TPA fabrication to120 nm,far beyond the diffraction limit of the 780 nm laser source.1 The essential mechanism of this nanoscale fabrication lies in the nonlinear effect,in which TPA-induced photopolymerization occurs only in the vicinity of the focal spot.展开更多
Non-Hermitian(NH)systems have revealed unique topological phenomena that are not observed in Hermitian counterparts,such as novel topology classifications and the NH skin effect.In periodic NH systems,eigenenergies be...Non-Hermitian(NH)systems have revealed unique topological phenomena that are not observed in Hermitian counterparts,such as novel topology classifications and the NH skin effect.In periodic NH systems,eigenenergies become complex and exhibit windings in the complex plane,while eigenstate winding numbers,which are strictly integers in Hermitian systems,can take half-integer values.However,direct experimental observation of NH winding of both eigenenergies and eigenstates,especially the half-integer winding,remains a significant challenge.In this work,we utilize the orbital angular momentum(OAM)synthetic dimension to construct an NH topological lattice and achieve direct observation of both eigenstate and eigenenergy windings.We report the first experimental observation of a half-integer eigenstate winding number,and reveal the intrinsic relationship between the direction in the NH skin dynamics and eigenenergy windings.Furthermore,by partitioning the OAM chain into two semi-infinite chains,we observe zero boundary modes and demonstrate that their distributions are jointly determined by the winding numbers of both the eigenstates and eigenenergies.This work provides comprehensive insights into NH topologies and offers a new experimental platform for exploring NH phenomena.展开更多
基金supported by the National Key R&D Program of China(no.2022YFB4600400)the National Natural Science Foundation of China(nos.T2325014,62205174,and 623B2042).
文摘Since the 1990s,femtosecond laser two-photon absorption(TPA),which enables point-by-point photopolymerization,has been a tool for making threedimensional(3D)microstructures.Approximately 10 years later,Kawata et al.improved the spatial resolution of TPA fabrication to120 nm,far beyond the diffraction limit of the 780 nm laser source.1 The essential mechanism of this nanoscale fabrication lies in the nonlinear effect,in which TPA-induced photopolymerization occurs only in the vicinity of the focal spot.
基金supported by the Innovation Program for Quantum Science and Technology(Grant Nos.2021ZD0301400 and 2021ZD0301200)the National Natural Science Foundation of China(Grants No.11874343,92365205,11974334,12404576,and W2411001)+3 种基金the Postdoctoral Innovative Talents Support program(BX20230349)China Postdoctoral Science Foundation Funded Project(2024M763125)Xiaomi Young Talents Program,the Fundamental Research Funds for the Central Universities(Grant No.WK2030000085)the USTC Major Frontier Research Program(Grant No.LS2030000002).
文摘Non-Hermitian(NH)systems have revealed unique topological phenomena that are not observed in Hermitian counterparts,such as novel topology classifications and the NH skin effect.In periodic NH systems,eigenenergies become complex and exhibit windings in the complex plane,while eigenstate winding numbers,which are strictly integers in Hermitian systems,can take half-integer values.However,direct experimental observation of NH winding of both eigenenergies and eigenstates,especially the half-integer winding,remains a significant challenge.In this work,we utilize the orbital angular momentum(OAM)synthetic dimension to construct an NH topological lattice and achieve direct observation of both eigenstate and eigenenergy windings.We report the first experimental observation of a half-integer eigenstate winding number,and reveal the intrinsic relationship between the direction in the NH skin dynamics and eigenenergy windings.Furthermore,by partitioning the OAM chain into two semi-infinite chains,we observe zero boundary modes and demonstrate that their distributions are jointly determined by the winding numbers of both the eigenstates and eigenenergies.This work provides comprehensive insights into NH topologies and offers a new experimental platform for exploring NH phenomena.
