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Physical Review Letters

Transition from Flat-Band Localization to Anderson Localization in a One-Dimensional Tasaki Lattice

Chao Zeng, Yue-Ran Shi, Yi-Yi Mao, Fei-Fei Wu, Yan-Jun Xie, Tao Yuan, Wei Zhang, Han-Ning Dai, Yu-Ao Chen, Jian-Wei Pan

Published Feb 5, 2024• 19 citations
Publisher

Abstract

We report an extensive experimental investigation on the transition from flat-band localization (FBL) to Anderson localization (AL) in a one-dimensional synthetic lattice in the momentum dimension. By driving multiple Bragg processes between designated momentum states, an effective one-dimensional Tasaki lattice is implemented with highly tunable parameters, including nearest-neighbor and next-nearest-neighbor coupling coefficients and onsite energy potentials. With that, a flat-band localization phase is realized and demonstrated via the evolution dynamics of the particle population over different momentum states. The localization effect is undermined when a moderate disorder is introduced to the onsite potential and restored under a strong disorder. We find clear signatures of the FBL-AL transition in the density profile evolution, the inverse participation ratio, and the von Neumann entropy, where good agreement is obtained with theoretical predictions.

DOI
10.1103/physrevlett.132.063401

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We report an extensive experimental investigation on the transition from flat-band localization (FBL) to Anderson localization (AL) in a one-dimensional synthetic lattice in the momentum dimension. By driving multiple Bragg processes between designated momentum states, an effective one-dimensional Tasaki lattice is implemented with highly tunable parameters, including nearest-neighbor and next-nearest-neighbor coupling coefficients and onsite energy potentials. With that, a flat-band localization phase is realized and demonstrated via the evolution dynamics of the particle population over different momentum states. The localization effect is undermined when a moderate disorder is introduced to the onsite potential and restored under a strong disorder. We find clear signatures of the FBL-AL transition in the density profile evolution, the inverse participation ratio, and the von Neumann entropy, where good agreement is obtained with theoretical predictions.
The diffusion and localization of particles in lattice potentials are essential topics in the study of quantum states of matter. As two distinct mechanisms, flat-band localization (FBL) caused by destructive interference and Anderson localization (AL) by strong disorder can both prohibit particle transport and lead to an insulator state. The realization and characterization of the two different insulating phases necessitate the ability to shape the lattice potential and measure particle transport at the single-site level. By using spatial momentum as an artificial dimension, ultracold quantum gas in a momentum lattice provides an ideal platform to achieve single-site resolution. Here, we demonstrate that the transition from flat-band localization to Anderson localization can be realized and quantitatively studied in a Bose-Einstein condensate in a one-dimensional momentum lattice. The flat-band localization is realized in a one-dimensional Tasaki model, while the transition to Anderson localization is achieved by imposing a strong enough disorder potential and is characterized by stark features of particle transport from an initial state in an experimentally realistic finite-size system. Submitted in parallel with Zeng et al., this article provides experimental details on the realization of an effective model and preparation of the initial state as well as a theoretical study of the transition with experimental parameters.
We investigated the one-dimensional diamond ladder in the momentum lattice platform. By inducing multiple two- and four-photon Bragg scatterings among specific momentum states, we achieved a flat band system based on the diamond model, precisely controlling the coupling strength and phase between individual lattice sites. Utilizing two lattice sites couplings, we generated a compact localized state associated with the flat band, which remained localized throughout the entire time evolution. We successfully realized the continuous shift of flat bands by adjusting the corresponding nearest neighbor hopping strength, enabling us to observe the complete localization process. This opens avenues for further exploration of more complex properties within flat-band systems, including investigating the robustness of flat-band localized states in disordered flat-band systems and exploring many-body localization in interacting flat-band systems.
Aharonov-Bohm (AB) caging, a special flat-band localization mechanism, has spurred great interest in different areas of physics. AB caging can be harnessed to explore the rich and exotic physics of quantum transport in flatband systems, where geometric frustration, disorder, and correlations act in a synergetic and distinct way than that in ordinary dispersive band systems. In contrast to the ordinary Anderson localization, where disorder induces localization and prevents transport, in flat band systems disorder can induce mobility, a phenomenon dubbed inverse Anderson transition. Here, we report on the experimental realization of the AB cage using a synthetic lattice in the momentum space of ultracold atoms with tailored gauge fields, and demonstrate the geometric localization due to the flat band and the inverse Anderson transition when correlated binary disorder is added to the system. Our experimental platform in a many-body environment provides a fascinating quantum simulator where the interplay between engineered gauge fields, localization, and topological properties of flat band systems can be finely explored.
Ultracold atoms in quasiperiodic lattices offer a versatile platform for studying many intriguingly disorder-driven phenomena. Here we study the quantum transport of noninteracting ultracold 133 Cs atoms in a one-dimensional quasiperiodic momentum lattice, which is formed by using the laser-coupled momentum states as synthetic dimensions. Through measurements of the site-resolved density distribution of atoms in the synthetic quasiperiodic lattice, we directly observe the transition from the atomic diffusive transport to Anderson localization in the initial injection site with increasing strength of the quasiperiodic modulation. We show the dependence of momentum width characterizing the atomic expansion degree on the quasiperiodic modulation strength, and our observation is in good agreement with the theoretical calculation. Our work provides significant insights for understanding the quantum spreading in disordered systems.
We systematically study the effect of disorder and interactions on a quasi-one-dimensional diamond chain possessing flat bands.Disorder localizes all the single-particle eigenstates, while at low disorder strengths, we obtain weak flat-band based localization (FBL), at high disorder strengths, we see conventional Anderson localization (AL).The compactly localized (CL) eigenstates of flat bands show a persisting oscillatory recurrence in the study of single-particle wave-packet dynamics.For low disorder, a damped oscillatory recurrence behavior is observed which is absent for high disorder.Noninteracting many-particle fermion states also follow the same trend except showing a delocalizing tendency at intermediate disorder due to the fermionic statistics in the system.As interactions are switched on, for the finite sizes that we are able to study, a nonergodic "mixed phase" is observed at low disorder which is separated from the MBL phase at high disorder by a thermal phase at intermediate disorder.A study of many-body nonequilibrium dynamics reinforces these findings.
Building on the development of momentum state lattices (MSLs) over the past decade, we introduce a simple extension of this technique to higher dimensions. Based on the selective addressing of unique Bragg resonances in matter-wave systems, MSLs have enabled the realization of tight-binding models with tunable disorder, gauge fields, non-Hermiticity, and other features. Here, we examine and outline an experimental approach to building scalable and tunable tight-binding models in two dimensions describing the laser-driven dynamics of atoms in momentum space. Using numerical simulations, we highlight some of the simplest models and types of phenomena this system is well-suited to address, including flat-band models with kinetic frustration and flux lattices supporting topological boundary states. Finally, we discuss many of the direct extensions to this model, including the introduction of disorder and non-Hermiticity, which will enable the exploration of new transport and localization phenomena in higher dimensions.