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ALOGLADIS Report Summary

Project ID: 256294
Funded under: FP7-IDEAS-ERC
Country: France

Final Report Summary - ALOGLADIS (From Anderson localization to Bose, Fermi and spin glasses in disordered ultracold gases)

The ERC-Starting grant project ALoGlaDis covers a series of works on the theory of ultracold-atom quantum systems in disordered fields, which may be divided into three researches lines.
The first research line deals with Anderson localization of ultracold matterwaves. Analytic theory of linear matterwaves in correlated disorder is developed. It reveals strong effects of tailored correlations and anisotropies. In one dimension, exact theory is devised, which shows that appropriate design of correlations yields original localization behavior, for instance enhancement of localization at higher energy. Significant deviation from pure exponential decay was also demonstrated. In dimension higher than one, approximate theory is developed with particular emphasis on anisotropic disorder. It permitted to identify clear localization signatures. The first non-debated observation of three-dimensional Anderson localization of a matter wave is eventually reported in a collaborative work with an experimental group. Theoretical calculations performed in the framework of the project yield fair agreement with experimental observations and pointed out significant deviation fromwidely-used estimates of the Anderson mobility edge. The latter are traced back to significant disorder-induced energy shift, that is calculated for the first time.
The second research line deals with Anderson localization in interacting Bose superfluids. While most studies now focus on the breaking of ergodicity as induced by disorder in interacting quantum systems, an original approach is pursued. The central question is to understand whether the interplay of disorder and interactions can allow for transport of quantum correlations and information. The analytic theory of quantum transport in interacting Bose superfluids is developed in arbitrary dimension. It is found that, while the ground state is fully delocalized, the many-body excitations can support Anderson localization and break Lieb-Robinson ballistic transport. In one dimension, exact calculations, supported by direct numerics, unambiguously demonstrate localization. Characteristic features that strongly differ from those of non-interacting particles are found. While similar physics occurs in two dimensions, it is shown that three dimensions support non-universal physics. Four classes of mobility spectra are hence identified, which depend not only on the relative strength of disorder and interactions but also on the model of disorder. In quasi-periodic structures, it is shown that interactions completely change the localization universality class. Signatures of localization in many-body systems are proposed, which pave the way to future theoretical and experimental work.
The third research line deals with superfluid-insulator transitions in strongly-interacting Bose gases at equilibrium. Quantum Monte Carlo approaches are developed within path-integral worm algorithms. The phase diagram of two-dimensional Bose gases in the presence of continuous-space disorder is worked out for the first time. The superfluid-insulator transition is shown to belong to the Berezinskii-Kosterlitz-Thouless universality class up to large disorder where no superfluid can be stabilized, and the critical temperature is calculated with high precision. In colaboration with an experimental group in Europe, the Mott transitions in one-dimensional Bose gases in arbitrary weak periodic potentials are studied. Numerical calculations validate field-theoretic calculations and pine point both the Mott-d and the Mott-U transitions. Significant deviations of the transition line compared to widely-used calculations are clearly shown both numerically and experimentally. This effect is traced back to significant renormalization of the Tomonaga-Luttinger parameters induced by even arbitrary weak periodic potentials. Excellent quantitative agreement with experimental data is reported, which validates such experiments as operational quantum simulators.

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