Non-hermitian Manipulation And Topological State Transport In One-dimensional Topological Systems

Hermiticity is a basic assumption of quantum mechanics,which guarantees that the system has real eigenvalues and satisfies unitary evolution.However,there is inevitable energy exchange between the system and the environment in practice,it is of universal significance to study the open systems described by the non-Hermitian Hamiltonian.In particular,the non-Hermitian systems exhibit some hallmark features with no counterpart in the traditional Hermitian case,such as complex energy spectrum,non-orthogonal eigenvector,exceptionl point and non-Hermitian skin effect.Moreover,non-Hermiticity introduces new modulation dimensions and symmetries,providing new ideas for studying novel physical effects.These unique non-Hermitian properties give rise to many anomalous and interesting phenomena,including topological lasers,enhanced sensing,nonreciprocal light propagation,coherent perfect absorption,unidirectional amplification.So far,with the development of classical wave system and quantum technology,non-Hermitian related physics have been demonstrated in optics,acoustics,atoms,superconducting circuits and other physical systems.The interplay of topology and non-Hermiticity opens a new avenue for engineering novel topological matter and generating various unique effects.As the most prototypical models allowing for nontrivial topological phases,the Su-Schrieffer-Heeger models have been widely used for non-Hermitian extensions by introducing various dissipative effects.The associated non-Hermitian Hamiltonian usually contains complex on-site potential or non-reciprocal hoppings.Both of these two cases allow the realization of exotic topological phenomena with no Hermitian counterparts,such as anomalous edge states,non-Bloch bulk-boundary correspondence,and non-Hermitian localization transitions.The present thesis mainly investigates non-Hermiticity-modulated topological phases and topological state transport in one-dimensional topological systems.The main resuls are orgnized as follows:(1)We demonstrate that the non-Hermiticity can induce rich topological phase transitions in a long-range Su-Schrieffer-Heeger model.We find that the non-Hermiticity is able to drive topological transitions between different winding numbers:v = 0 → 1 and 2 → 1.These topological phase transitions can be characterized by the bulk band gap,edge states,complex Zak phase,and hidden Chern number.Interestingly,by extending to more general long-range Su-Schrieffer-Heeger lattices,the non-Hermiticity can drive exotic transitions associated with the corresponding Hermitian topological phases.Finally,we demonstrate the experimental feasibility of our scheme in an electric circuit system.(2)We investigate the interplay of the uniform flux and the on-site gain and loss by considering a dissipative two-leg ladder model.By calculating the spectral winding number and the generalized Brillouin zone,we predict the non-Hermitian skin effect,whose skin modes display the bipolar localization.This skin effect emerges when the flux is not an integer multiple of π.We further demonstrate the breakdown of the chiral currents due to the presence of the skin effect by studying single-particle dynamics.Moreover,we show that the non-Hermiticity can drive a flux-dependent topological transition characterized by a hidden Chern number.(3)By considering a nonreciprocal dimerized lattice with staggered quasiperiodic disorder,we find that the localization transition can appear twice by increasing the disorder strength.We also unravel a multi-complex-real eigenenergy transition,whose transition points coincide with those in the localization phase transitions.Moreover,the impacts of boundary conditions on the localization properties have been clarified.Finally,we study the wavepacket dynamics in different parameter regimes,which offers an experimentally feasible route to detect the reentrant localization.(4)We experimentally demonstrate a novel adiabatic pumping scheme,topological pumping of defect state,by introducing a Fock photonic lattice,which is a classical analogue of Fock-state lattice of two-mode Jaynes-Cummings model.Since this pumping is always protected by an energy gap even for a large size of the system,its pumping efficiency can be enhanced considerably compared with the conventional topological pumping schemes.Moreover,a topologically-protected beam splitter is also realized by designing the pumping channels of defect state.The experimental results agree well with theoretical simulations.