Disorder and Quantum Magnetism in Ultracold Atom Systems

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This project aims at a theoretical description of quantum magnetism and disorder effects in strongly interacting Bose- and Fermi gases with multiple components. Due to impressive progress in experiments on cold gases during the last few years, the disordered three-dimensional Bose-Hubbard model can now be simulated in the laboratory, Mott-insulating states of fermions have been realized, and achieving long-range magnetic order is currently one of the major goals in the field. Quantitative theoretical predictions on quantum phases and their critical parameters are therefore becoming essential for further guidance of experiments. However, a reliable description of these systems especially in higher dimensions is still a major theoretical challenge.Based on successful method development during the first funding period, we are now able to quantitatively describe fermionic and bosonic quantum lattice gases, in the presence of external potentials and/or disorder, at any correlation strength, and for experimentally realistic system sizes.Our focus in the second funding period is on systems which are realized in the experimental groups of this research unit: spinor bosons, heteronuclear molecules, and Fermi-Fermi mixtures with mass imbalance. We aim at quantitatively describing phases with long-range order such as tunable antiferromagnetism, supersolids and polaronic phases, and their modification in the presence of experimentally realizable speckle disorder or incommensurate superlattices, where qualitatively new phases such as Bose glasses or spin liquids can emerge. The crucial influence of different lattice geometries such as triangular, or spin-dependent hexagonal will be studied as well.A major goal of this project is to extract spectroscopic signatures of these quantum phases, which are measurable in 2-photon Bragg scattering, RF spectroscopy or by stimulated Raman scattering. We will calculate the associated 1- and 2-particle response quantities within our non-perturbative techniques based on dynamical mean-field theory. In this way we hope to aid experimental detection of correlated many-body phases and also their precursor effects above the critical temperature.