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Disordered Ultra-Cold Atoms

Final Report Summary - DUCA (Disordered Ultra-Cold Atoms)

One of the main unsolved problems in condensed matter physics is the interplay between disorder and interactions. Theoretical and experimental progress has been slow due to the intrinsic difficulties to control all relevant variables. Recent progress in the field of ultracold atomic gases, with Europe playing a leading role, paves the way towards highly controlled investigations of this many-body physics. The purpose of this project was to bring a young researcher experienced in cold atom physics to Rome to work within a condensed matter theory group which has played a leading role in the development of the theory of interacting and disordered electron systems. The objective was the transfer of knowledge between condensed matter and cold atom physics which could significantly advance both fields.

The two-year project aimed at a reformulation of the scaling theory of disordered electron systems for ultra-cold atoms, the study of the interplay between quantum chaos and interactions and the investigation of dirty superconductors. Because the young researcher has won at early stage a permanent position as a researcher in France, the project was abbreviated to seven months and has focused on one of the three aspects originally planned: the study of disordered superconductors. A current activity in the host group concerns superconductors with strong disorder, a problem closely related to the issue of high-Tc superconductivity. Disordered fermionic ultracold atoms could permit to answer fundamental questions in this problem. Experiments with two-component Fermi gases with interactions controlled by Feshbach resonances have allowed for studies of the so-called BEC-BCS crossover. The introduction of an additional disordered potential could permit to study the superconductor-insulator transition.

Motivated by this perspective, the researcher has studied the superconductor-insulator transition which nature is still under debate. Recently, a new theory based on the cavity method was formulated which allows to give an analytical description of this quantum phase transition in terms of glassy physics. It is based on an effective spin model and rely on some approximations, which he has studied the validity and relevance. He has started from a microscopic model of a disordered superconductor, the disordered attractive Hubbard model, and has compared the results of his numerical simulations with the predictions of this theory. His results have confirmed the proposed approach but invalidated certain crucial approximations. He has also compared his results to previously published experimental data and found a good agreement.

The results were obtained in a fruitful collabouration between the host group and the researcher. The study he has carried on should help clarifying the precise nature of the superconductor-insulator transition and allow making predictions for future experiments, both with condensed matter and ultra-cold atoms setups. A letter is being finalised.