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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$J_n\propto n^{\sigma}$,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$\sigma$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.
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关键词:
- Anderson局域化 /
- 弯曲时空 /
- 超冷原子 /
- 动量态晶格
Anderson localization is a profound phenomenon in condensed matter physics, representing a fundamental transition of eigenstates induced 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 growing interest in quantum lattice models in curved spacetime (CST), the AAH model in CST has been proposed as a way to explore the interplay between Anderson localization and CST physics. While a few CST lattice models have been realized in optical waveguide systems to date, significant challenges remain in the experimental preparation and measurement of states, primarily due to the difficulty of dynamically modulating lattices in such systems. In this study, 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. Thanks to the individual controllability of the coupling between each pair of adjacent momentum states, the coupling amplitude in the MSL can be encoded as a power-law position-dependent form $J_n \propto n^{\sigma}$, facilitating effective simulation of CST. Numerical calculation results of the MSL Hamiltonian show an emergence of the phase separation in a 34-site AAH chain in CST, where wave packet dynamics exhibit localized behavior on one side of the critical site and extended behavior on the other. The phase separation critical site is observed by extracting turning points of the evolving fractal dimension and the wave packet width derived from evolution dynamic simulations. Furthermore, by modulating the spacetime curvature parameter $\sigma$, we propose a method for eigenstates preparation of the AAH chain in CST, and perform numerical simulations in the MSL. Through calculating the fractal dimension of eigenstates prepared following the aforementioned method, we analyze the localization properties of eigenstates under various quasiperiodic modulation phases, confirming the coexistence of localized phase, swing phase, and extended phase in the energy spectrum. Unlike traditional localized and extended phases, eigenstates in the swing phase of the AAH model in CST exhibit different localization properties under different modulation phases, indicating the prescence of a swing mobility edge. Our results provide a feasible experimental approach to study Anderson localization in CST and introduce a new platform for realizing quantum lattice models in curved spacetime.-
Keywords:
- Anderson localization /
- curved spacetime /
- ultracold atoms /
- momentum-state lattice
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