Recent experiments in noninteracting ultracold atoms in three-dimensional speckle potentials have yielded conflicting results regarding the so-called mobility edge, i.e., the energy threshold separating Anderson localized from diffusive states. At the same time, there are theoretical indications that most experimental data overestimate this critical energy, sometimes by a large amount. Using extensive numerical simulations, we show that the effect of anisotropy in the spatial correlations of realistic disorder configurations alone is not sufficient to explain the experimental data. In particular, we find that the mobility edge obeys a universal scaling behavior, independently of the speckle geometry.
Recent experiments in noninteracting ultracold atoms in three-dimensional speckle potentials have yielded conflicting results regarding the so-called mobility edge, i.e., the energy threshold separating Anderson localized from diffusive states. At the same time, there are theoretical indications that most experimental data overestimate this critical energy, sometimes by a large amount. Using extensive numerical simulations, we show that the effect of anisotropy in the spatial correlations of realistic disorder configurations alone is not sufficient to explain the experimental data. In particular, we find that the mobility edge obeys a universal scaling behavior, independently of the speckle geometry.
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.
We study the critical dynamics of matter waves at the three-dimensional Anderson mobility edge in cold-atom disorder quench experiments. General scaling arguments are supported by precision numerics for the spectral function, diffusion coefficient, and localization length in isotropic blue-detuned speckle potentials. We discuss signatures of critical slowdown in the time-dependent central column density of a spreading wave packet, and evaluate the prospects of observing anomalous diffusion right at criticality.
We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are determined as a function of the disorder strength, ranging from vanishing disorder up to the critical disorder intensity where the two mobility edges merge and the whole band becomes localized. Our theoretical analysis is based both on continuous-space models that take into account the details of the spatial correlation of the speckle pattern, and also on a simplified tight-binding model with an uncorrelated distribution of the on-site energies. The mobility edges are computed via the analysis of the energy-level statistics, and we determine the universal value of the ratio between consecutive level spacings at the mobility edge. We analyze the role of the spatial correlation of the disorder, and we also discuss a qualitative comparison with available experimental data for interacting atomic Fermi gases obtained in the moderate interaction regime.
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.
Anderson Localization - the complete halt of wave transport through multiple scattering and phase coherence - was discovered in 1958 and has been actively studied since then with several types of waves (light, µ-waves, ultrasound, acoustic waves, etc.). In three-dimensional systems, Anderson Localization manifests as a phase transition around a critical energy - the Mobility Edge - that separates the localized (insulator) states from the diffusive (metallic) states.Ultracold atoms are promising candidates for such experiments, and various groups have reported evidence of the 3D Anderson Transition, in particular, our group in 2012. Nevertheless, all these preliminary measurements were limited by the unwanted broadening of the energy distribution when the atoms were transferred into the disorder. Hence, no direct observation of the transition could be achieved.The quest for the direct observation of the 3D Anderson Transition has motivated us to develop a novel spectroscopic scheme using state-dependent disorder. The concept is to transfer, via RF coupling, a small fraction of a Bose-Einstein Condensate from a disorder-insensitive state to a disorder-sensitive state. By doing so, we selectively populate targeted energy levels in the disorder with a narrow energy distribution. This technique has paved the way for successfully achieving the direct observation of the 3D Anderson Transition in a 3D laser speckle. Moreover, it yields a precise measurement of the Mobility Edge, which is in excellent agreement with the numerical predictions.The heart of our achievement lies in the spectroscopic scheme. When transferring only a few atoms, we expect the coupling of a discrete state to a continuum, leading to a Fourier-limited energy distribution. This key assumption has so far been verified only indirectly, but never tested numerically. In the last part of my PhD, I have set up the framework for the numerical description of the RF transfer scheme. While the study remains preliminary, it already demonstrates that the dynamics can be more subtle than expected, and the model deserves further attention in the future.
The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself.This dependence is rich in counter-intuitive consequences.It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present.In this work, we apply a perturbative microscopic transport theory and the self-consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic two-dimensional (2D) and three-dimensional (3D) speckle potentials.In particular, we discuss the anisotropy of single-scattering, diffusion and localization.We also calculate disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalizing energies in the standard on-shell approximation.We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge).We illustrate the theoretical findings with examples which are relevant for current matter wave experiments, where the disorder is created with laser speckle.This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D.