Measurement of the mobility edge for 3D Anderson localization

Abstract: Anderson localization is a universal phenomenon affecting non-interacting quantum particles in disorder. In three spatial dimensions it becomes particularly interesting to study because of the presence of a quantum phase transition from localized to extended states, predicted by P.W. Anderson in his seminal work, taking place at a critical energy, the so-called mobility edge. The possible relation of the Anderson transition to the metal-insulator transitions observed in materials has originated a flurry of theoretical studies during the past 50 years, and it is now possible to predict very accurately the mobility edge starting from models of the microscopic disorder. However, the experiments performed so far with photons, ultrasound and ultracold atoms, while giving evidence of the transition, could not provide a precise measurement of the mobility edge. In this work we are able to obtain such a measurement using an ultracold atomic system in a disordered speckle potential, thanks to a precise control of the system energy. We find that the mobility edge is close to the mean disorder energy at small disorder strengths, while a clear effect of the spatial correlation of the disorder appears at larger strengths. The precise knowledge of the disorder properties in our system offers now the opportunity for an unprecedented experiment-theory comparison for 3D Anderson localization, which is also a necessary step to start the exploration of novel regimes for many-body disordered systems.

Measurement of the Mobility Edge for 3D Anderson Localization

This paper presents a significant contribution to the study of 3D Anderson localization, specifically focusing on the accurate measurement of the mobility edge in ultracold atomic systems subjected to disordered potentials. Anderson localization, a phenomenon where non-interacting quantum particles become trapped in random potentials, has intrigued researchers due to its implications in metal-insulator transitions observed in materials.

The authors leverage an ultracold atomic system with disordered speckle potentials, allowing precise control of system energy to measure the mobility edge. The experimental setup involves loading a Bose-Einstein condensate of $^{39}$K atoms into a disordered optical speckle field, carefully adjusting parameters using a Feshbach resonance to manage atom interactions. This meticulous preparation provides a conducive environment to observe localization transitions predicted by Anderson's theory. The results demonstrate a nearly linear scaling of the mobility edge with the disorder strength at lower intensities, followed by notable deviations as the disorder strength increases beyond a certain threshold set by spatial correlations.

Experimental Insights and Results

The study introduces a novel method to control energy dispersions within the atomic system, crucial for determining the mobility edge. Key experimental procedures involve:

1. Controlled Loading: The Bose-Einstein condensate is adiabatically loaded into the speckle potential, gradually decreasing interatomic interactions and external harmonic confinement while increasing disorder strength.

2. Energy Measurement: The authors estimate the energy distribution of the atomic samples by combining kinetic energy measurements with simulations of low-energy eigenstates. The adoption of time-dependent modulation for controlled excitations allows them to determine the energy required to break localization—shedding light on the mobility edge.

3. Excitation Spectrum Analysis: Experiments measuring atom number and kinetic energy against modulation frequencies reveal critical insights about the mobility edge. The obtained mobility edge values deviate from certain theoretical predictions, emphasizing the complexity and sensitivity of localized states to experimental conditions.

Implications and Future Directions

The paper suggests that precise knowledge of the disorder properties may enable unrivaled comparisons between experimental and theoretical results governing 3D Anderson localization. This comparison is vital for further exploration of complex quantum phase transitions in disordered many-body systems.

The presence of exact control over the experimental parameters may catalyze investigations into many-body localization, anomalous diffusion phenomena, and the peculiarities of Bose-Einstein condensates under disorder—a burgeoning area where theoretical predictions remain exceptionally challenging. Complementary studies could extend to other types of disorder, offering broader implications for understanding non-interacting quantum systems.

In summation, the research methodology and refined techniques adopted in this paper highlight critical advances in the characterization of the mobility edge for 3D Anderson localization. By precisely correlating experimental data with theoretical models, researchers can deepen their understanding of quantum interference effects, potentially unlocking novel quantum regimes that have yet to be explored fully.