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.
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].
Realization of nonreciprocal transport is of great importance in the development of devices and systems that require the directional manipulation of signals or particles in information processing and modern physics. For ultracold atomic systems, the approaches based on synthetic dimensions have led to rapid advances in engineering quantum transport. Here, we use laser-coupled discrete momentum states of noninteracting ultracold atoms to synthesize a momentum lattice, and construct a closed ring with controllable tunneling phase in the momentum lattice. We measure the density evolution of atoms in the synthetic lattice with the single-site resolution, and observe the nonreciprocal dynamics by controlling the tunneling phase. We show the effect of both the applied phase and the coupling strength between two distinct population regions on the population distribution of atoms in the momentum lattice, and provide the optimal parameters for achieving the nonreciprocal transport.
Abstract In a recent experiment (Yu et al 2026 arXiv: 2602.07654 ), energy-resolved measurements of an atomic matter wave spreading in a speckle potential enabled the direct observation of the three-dimensional Anderson transition. In this work, we present a quantitative theoretical description of the matter-wave dynamics based on a tailored implementation of the self-consistent theory of localization, which incorporates both the spectral and spatial properties of the state prepared in the disorder. We benchmark this theoretical approach against ab initio numerical simulations, and use it to analyze the atom density profiles observed experimentally in the localized, diffusive, and critical regimes. Particular emphasis is placed on the key role of the atomic energy distribution, especially on the distinct contributions of Bose-condensed and thermal atoms to interpret the experimental profiles. Our framework provides a versatile and efficient theoretical toolbox for quantitatively describing wave-packet dynamics in three-dimensional disordered quantum systems, which remains challenging for state-of-the-art large-scale numerical simulations.
Ultracold atoms in optical lattices offer a unique platform for investigating disorder-driven phenomena. While static disordered site potentials have been explored in a number of experiments, a more general, dynamical control over site-energy and off-diagonal tunnelling disorder has been lacking. The use of atomic quantum states as synthetic dimensions has introduced the spectroscopic, site-resolved control necessary to engineer more tailored realisations of disorder. Here, we present explorations of dynamical and tunneling disorder in an atomic system by controlling laser-driven dynamics of atomic population in a momentum-space lattice. By applying static tunnelling phase disorder to a one-dimensional lattice, we observe ballistic quantum spreading. When the applied disorder fluctuates on time scales comparable to intersite tunnelling, we instead observe diffusive atomic transport, signalling a crossover from quantum to classical expansion dynamics. We compare these observations to the case of static site-energy disorder, where we directly observe quantum localisation.Cold atom quantum simulation has had challenges in realising the tailored, dynamic types of disorder relevant to real materials. Here, the authors use synthetic momentum-space lattices to engineer spatially and dynamically controlled disorder to observe ballistic, diffusive, and arrested atomic transport.
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling theory predicts a quantum phase transition at a critical energy, the mobility edge, separating localized from diffusive states and underpinning metal-insulator transitions in electronic systems. Despite decades of experimental efforts, a direct observation of this emblematic transition for matter waves has remained elusive. Previous attempts with ultracold atoms were hindered by strong and uncontrolled energy broadening, resulting in indirect, sometimes inaccurate, and model-dependent estimates of the mobility edge. Here we implement a novel energy-resolved scheme to prepare atomic matter waves with a narrow energy distribution and track their expansion dynamics over long timescales. This allows for a direct observation of the three-dimensional Anderson transition in a laser-speckle disordered potential, and for a precise measurement of the mobility edge that is independent of any underlying theoretical modeling. Our measurements show excellent agreement with state-of-the-art numerical predictions over a wide range of disorder strengths, resolving long-standing discrepancies between prior experiments and theory. Beyond the three-dimensional Anderson transition, our approach opens new avenues for quantitative investigations of quantum critical phenomena in spatially disordered systems, including the roles of dimensionality, symmetry class, and interactions.
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.