Localized Property And Quantum Transport In One-dimensional Disordered And Quasiperiodic Lattice Models

Quantum transport of matter waves in the presence of disorder has always been an important subject in condensed matter physics.Due to random disordered potential,the extended single-particle Bloch waves in a periodic lattice model can undergo a destructive-interference-induced quantum transition and thus become exponentially localized.This mechanism is commonly referred to as Anderson localization.In some deterministic potentials analogous to random disordered potential,localized single-particle state can also be obtained by a localization-delocalization transition determined by selfdual symmetry.The incommensurate potential in a quasiperiodic lattice model is a celebrated example and has been extensively studied with the standard Aubry-Andre model.Such potential has been demonstrated to show interesting quantum transport phenomena.For instance,the quasiperiodic lattice model can have a fractal spectrum.In addition,energy-dependent mobility edges,which separate extended and localized eigenstates at a critical energy and only appear in three-dimensional disordered systems,can exist in some one-dimensional quasiperiodic lattice models.However,beyond noninteracting quantum systems,the study and observation of the localized property of interacting particles in disordered lattice models are still lacking,and the study on quantum transport in quasiperiodic lattice models with mobility edges remains to be explored.For the purpose of addressing these questions,in this thesis,we study a one-dimensional disordered twoparticle lattice model and two one-dimensional quasiperiodic lattice models with mobility edges.Firstly,in a one-dimensional disordered lattice model,in order to explore the twoparticle localized property with nearest-neighbor interaction,via two experimentally measurable time-dependent physical quantities,i.e.,inverse participation ratio and spatial correlation,we systematically study Anderson localization of two bosons and two fermions with nearest-neighbor interaction for three types of initial conditions,short-time and longtime evolution scales,and two types of disorders.We find that the two-particle localization behavior characterized by the inverse participation ratio depends on the strength of the nearest-neighbor interaction,on the type of disorder,and on the initial condition,but is independent of the two-particle quantum statistical property,of the evolution time scale,and of whether the nearest-neighbor interaction is attractive or repulsive.Meanwhile,two-particle spatial correlation indicates more novel and unique features.In the ordered case,two types of two-boson binding phenomena and bosonic "fermionization"phenomenon are shown,which are all attributed to the band structure of the system.In the disordered case,we reexamine the effect of the nearest-neighbor interaction on the twoparticle Anderson localization and the joint effect of disorder and the nearest-neighbor interaction is revealed.Furthermore,by employing an initial condition that breaks one of two specific symmetries,we further demonstrate that the independence of the inverse participation ratio or the spatial correlation on the sign of the nearest-neighbor interaction strength can be eliminated,so that we can discriminate the nearest-neighbor attractive and repulsive interactions.Finally,these results can be directly observed in a two-dimensional disordered linear coupled optical waveguide array,and we illustrate the relevant details of its experimental implementation.Secondly,in order to reveal the effect of the occurrence of Anderson localization and the presence of mobility edges on the adiabatic pumping between topological boundary modes in one-dimensional quasiperiodic lattices,in a one-dimensional generalized Aubry-Andre model with mobility edge,by engineering and resorting to two end-bulkend channels,we study the adiabatic pumping between left and right end modes.We find that as the mobility edge is introduced,the whole system can be in an intermediate regime mixed with localized and extended phases,and even when the parameter determining the localization-delocalization transition exceeds the threshold of the standard Aubry-Andre model,one of the channels can remain intact,leading to that the critical condition for successful pumping in this channel is relaxed.Moreover,widening the range of the hybrid phase region can enhance the effect of the mobility edge on the adiabatic pumping.In order to validate these conclusions,based on fidelity,the pumping result is quantified,and the corresponding pumping process is also examined.By engineering another channel,we further realize a flexible adiabatic pumping among four types of generalized end modes.Finally,in order to further elucidate the effect of Anderson localization and mobility edges on the transport characteristics of the system,in a one-dimensional quasiperiodic lattice model with mobility edge,we study the problem of quantum transport,i.e.,topological pumping between edge modes and boundary excitation transfer.On the one hand,by resorting to two edge-bulk-edge channels,we realize the topological pumping between edge modes and demonstrate that the success or failure of the topological pumping depends on whether the corresponding bulk subchannel undergoes a localizationdelocalization transition.Compared with the standard Aubry-Andre model,we find that the introduction of the mobility edge can trigger an opposite outcome for successful pumping in these two channels,showing a discrepancy in the critical condition,and can improve the robustness of the topological pumping against quasidisorder.On the other hand,for the transfer between excitations at both boundaries of the lattice model,we find that an anomalous phenomenon characterized by the enhanced quasidisorder contributing to the boundary excitation transfer emerges.Furthermore,there exists a parametric regime where a nonreciprocal effect occurs in the presence of the mobility edge,which can lead to a unidirectional transport behavior for the boundary excitation transfer.