弯曲时空下的Aubry-André-Harper动量态链  

Aubry-André-Harper momentum-state chain in curved spacetime

作　　者：毛一屹 戴汉宁 MAO Yiyi;DAI Hanning(Hefei National Research Center for Physical Sciences at the Microscale,School of Physical Sciences,University of Science and Technology of China,Hefei 230026,China;Shanghai Research Center for Quantum Science,CAS Center for Excellence in Quantum Information and Quantum Physics,University of Science and Technology of China,Shanghai 201315,China;Hefei National Laboratory,Hefei 230088,China)

机构地区：[1]中国科学技术大学物理学院,合肥微尺度物质科学国家研究中心,合肥230026 [2]中国科学技术大学,中国科学院量子信息与量子科技创新研究院,上海量子科学研究中心,上海201315 [3]合肥国家实验室,合肥230088

出　　处：《物理学报》2025年第2期75-83,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12074367);国家重点研发计划(批准号:2020YFA0309804,2023YFC2206200);上海市市级科技重大专项(批准号:2019SHZDZX01);科技创新2030-“量子通信与量子计算机”重大项目(批准号:2021ZD0302002)资助的课题.

摘　　要：Anderson局域化是凝聚态物理中一个影响深远的现象,它代表了由无序引发的本征态的根本性转变.本文提出了一个基于超冷原子动量态晶格系统的实验方案,用以实现弯曲时空下的Aubry-André-Harper(AAH)模型,并研究其中的Anderson局域化.得益于每对相邻动量态之间耦合的单独可操控性,动量态晶格中的耦合强度可以被编辑成幂律位置依赖的形式J_(n)∝n^(σ),从而能够有效模拟弯曲时空.动量态晶格中波包演化的数值计算结果表现出初始格点依赖的局域化性质,符合理论预测的相分离现象.通过分析波包演化动力学数据,可以观测到相分离临界格点的移动.同时,本文还提出了通过调制时空弯曲参数σ来制备本征态的方案,并在动量态晶格中进行了数值仿真.最后,在不同准周期调制相位下制备能谱中所有本征态,分析了本征态的局域化性质,验证了在能谱中共存的局域相、延展相和摇摆相.本文为在实验中研究弯曲时空下的Anderson局域化物理提供了新的可行途径.Anderson localization is a profound phenomenon in condensed matter physics,representing a fundamental transition in eigenstates,which is triggered off by disorder.The one-dimensional Aubry-André-Harper(AAH)model,an iconic quasiperiodic lattice model,is one of the simplest models that demonstrate the Anderson localization transition.Recently,with the growth of interest in quantum lattice models in curved spacetime(CST),the AAH model in CST has been proposed to explore the interplay between Anderson localization and CST physics.Several CST lattice models have been realized in optical waveguide systems to date,but there are still significant challenges to the experimental preparation and measurement of states,primarily due to the difficulty in dynamically modulating the lattices in such systems.In this work,we propose an experimental scheme using a momentum-state lattice(MSL)in an ultracold atom system to realize the AAH model in CST and study the Anderson localization in this context.Due to the individually controllable coupling between adjacent momentum states in each pair,the coupling amplitude in the MSL can be encoded as a power-law position-dependent J_(n)∝n^(σ),which is conducive to the effective simulation of CST.The numerical calculation results of the MSL Hamiltonian show that the phase separation appears in a 34-site AAH chain in CST,where wave packet dynamics exhibit the localized behavior on one side of the critical site and the extended behavior on the other side.The critical site of phase separation is identified by extracting the turning points of the evolving fractal dimension and wave packet width from the evolution simulations.Furthermore,by modulating the spacetime curvature parameterσ,we propose a method of preparing the eigenstates of the AAH chain in CST,and perform numerical simulations in the MSL.By calculating the fractal dimension of eigenstates prepared using the aforementioned method,we analyze the localization properties of eigenstates under various quasiperiodic modulation phases,

关 键 词：ANDERSON 局域化 弯曲时空 超冷原子 动量态晶格 

分 类 号：O469[理学—凝聚态物理]