We report on the measurement of the spectral functions of noninteracting ultracold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by 2 orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The method relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for experimental investigations of three-dimensional Anderson localization.
We report on the measurement of the spectral functions of noninteracting ultracold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by 2 orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The method relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for experimental investigations of three-dimensional Anderson localization.
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.
Abstract: The ability to load ultracold atoms at a well-defined energy in a disordered potential is a crucial tool to study quantum transport, and in particular Anderson localization. In this paper, we present a new method for achieving that goal by rf transfer of atoms in an atomic Bose-Einstein condensate from a disorder-insensitive state to a disorder-sensitive state. It is based on a bichromatic laser speckle pattern, produced by two lasers whose frequencies are chosen so that their light-shifts cancel each other in the first state and add up in the second state. Moreover, the spontaneous scattering rate in the disorder-sensitive state is low enough to allow for long observation times of quantum transport in that state. We theoretically and experimentally study the characteristics of the resulting potential.
We report on the impact of variable-scale disorder on 3D Anderson localization of a noninteracting ultracold atomic gas. A spin-polarized gas of fermionic atoms is localized by allowing it to expand in an optical speckle potential. Using a sudden quench of the localized density distribution, we verify that the density profile is representative of the underlying single-particle localized states. The geometric mean of the disordering potential correlation lengths is varied by a factor of 4 via adjusting the aperture of the speckle focusing lens. We observe that the root-mean-square size of the localized gas increases approximately linearly with the speckle correlation length, in qualitative agreement with the scaling predicted by weak scattering theory.
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.
We study Anderson localization of ultracold atoms in weak one-dimensional speckle potentials using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between energy regions where localization lengths differ by orders of magnitude. We also point out that the correction to the Born term explicitly depends on the sign of the potential. Our results are in agreement with numerical calculations in a regime relevant for experiments. Finally, we analyze our findings in the light of a diagrammatic approach.
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.