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.
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 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.
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.
Anderson localization of waves in disordered media was originally predicted[1] fifty years ago, in the context of transport of electrons in crystals[2]. The phenomenon is much more general[3] and has been observed in a variety of systems, including light waves[4, 5]. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization[6]. Here we use a non-interacting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice - a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases[8, 9].
We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.
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.
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.