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Chinese Physics B

Observation of flat-band localized state in a one-dimensional diamond momentum lattice of ultracold atoms

Chao 超 Zeng 曾, Yue-Ran Shi, Yi-Yi 一屹 Mao 毛, Fei-Fei 菲菲 Wu 武, Yan-Jun 岩骏 Xie 谢, Tao 涛 Yuan 苑, Han-Ning Dai, Yu-Ao Chen

Published Nov 16, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ad0cd1

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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.
The presence of flat bands is a source of localization in lattice systems. While flat bands are often unstable with respect to interactions between the particles, they can persist in certain cases. We consider a diamond ladder with transverse hopping that possesses such stable flat bands and show that many-body localization appears in the presence of interactions without quenched disorder. We numerically demonstrate that the eigenstate thermalization hypothesis is violated. We show that the influence of degenerate flat band states spreads across the full energy spectrum and grows extensively in the thermodynamic limit. Furthermore, we verify localization in terms of time evolution of some local observable, revival probability, participation ratio, and entanglement entropy.
The realization of robust quantum storage devices relies on the ability to generate long-lived, spatially localized states. In this Letter, we introduce a method for the targeted creation of compact excitations in flat-band lattices. By injecting in-plane radiation waves from the system's edge and applying a localized on-site potential at the desired storage position, we induce hybridization between compact localized states of the flat band and resonant dispersive plane waves. This hybridization enables the formation of spatially compact, stable excitations suitable for quantum memory applications. We experimentally validate this mechanism using photonic waveguide arrays, focusing on two representative geometries: the diamond chain and the one-dimensional Lieb ladder. Our approach is broadly applicable to any platform supporting flat-band physics.
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.
Symmetry plays a crucial role in understanding topological phases in materials. In one-dimensional systems, such as the Su-Schrieffer-Heeger (SSH) model, chiral symmetry is thought to ensure the quantization of the Zak phase and the nontrivial topological phase. However, our work demonstrates that the one-dimensional lattice system with broken chiral symmetry can still possess quantized Zak phase and nontrivial topological phase. Specifically, we use a Bose-Einstein condensate of 87Rb atoms in a momentum space lattice of ultracold atoms to effectively simulate a one-dimensional Zigzag model of 26 sites, which intrinsically breaks the chiral symmetry by additional next-nearest-neighbor coupling. To ensure the existence of the nontrivial topological phase, where the Zak phase can be measured from the time-averaged displacement during the system’s evolution, we need to preserve the inversion symmetry by modulating laser power so that all next-nearest-neighbor coupling strengths are equal. Furthermore, by changing the ratio of nearest-neighbor coupling strengths, we observe a topological phase transition from a nontrivial topological phase to a trivial topological phase at the point where the ratio equals 1. Our work demonstrates that the ultracold atom system provides a controllable platform for studying the symmetrical phase and topological phase, with the potential to explore nonlinear topological phenomena by increasing the interactions among atoms. In addition, our system can be used to investigate other interesting topological phenomena with more complex models, such as critical phenomena at the phase transitions and flat band structures in the extended SSH model with long-range coupling. By controlling the coupling strengths, we can also explore the influence of different symmetries on the topological properties of extended SSH models in the future. Moreover, our platform makes it possible to studythe models with more energy bands, such as the Aharonov-Bohm caging model with a three-level structure, which shows peculiar flat-band properties. This work provides opportunities for various studies in the fields of symmetry, topology, and the interaction of controllable quantum systems.
Abstract We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced many-body localizated phase. Physical picture of this crossover is investigated in detail. We also observe non-ergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.