Interaction, Disorder and Dynamical Effects in Strongly Correlated Bosonic and Fermionic Ultracold Quantum Gases

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Ultracold bosonic and fermionic quantum gases in optical lattices have proven to be a novel and highly useful class of experimental systems in which the effect of strong correlation physics in a many-body setting can be explored. The almost one-to-one implementation of fundamental model Hamiltonians in such systems has allowed one to perform ab-initio comparisons between state of the art solid-state analytical and numerical methods with experiments, thus enabling in many cases a first quantitative test of such theories. In addition, ultracold quantum gases offer unique opportunities for the investigation of non-equilibrium dynamics in strongly correlated quantum systems that enable the extension of our knowledge about strong correlation effects from a static to a dynamic regime.Within this research proposal we plan to focus on the investigation of fermionic quantum gas mixtures in an optical lattice, as well as on the behaviour of Bose-Fermi mixtures with variable many-body interactions in optical lattices. For repulsively interacting fermionic quantum gas mixtures our group has reached a fermionic Mott insulating phase during the first phase of the research group funding. We now plan to extend this work by implementing novel cooling schemes to reach an antiferromagneticly ordered phase for the two-component spin mixture. The realization of optical superlattices in this setup will allow us to prepare and analyze the magnetic ordering of the fermionic quantum gas especially in the interesting temperature regime around TNéel, where the phase transition to an antiferromagnet occurs. Building on our previous work on attractively interacting fermionic quantum gas mixtures, we plan to demonstrate a superfluid phase within the lowest band of an optical lattice. Recent theoretical work has shown that the use of an attractively interacting Fermi gas mixture can provide experimental advantages, and can even yield insight into the investigation of the repulsively interacting Hubbard model. Furthermore, we plan to extend recent transport measurements for fermionic quantum gas mixtures, in which we have investigated the role of interactions on the transport behaviour of the system, towards the direction of controlled disorder. Here, in addition to variable interactions, we will introduce controllable static disorder potentials during the transport measurement. For Bose-Fermi mixtures we plan to realize polarons, in which single fermionic impurity atoms can be dressed by phononic excitations of the bosonic quantum gas. By tuning the interation strength between the fermions and bosons it should be possible to investigate the fundamental change in transport of such new quasiparticles.As a second main project part, we plan to continue our work on the non-equilibrium physics of one-dimensional bosonic quantum gas ladder systems realized using optical superlattices. Here we plan to investigate how dynamical concepts well known for a quantum mechanical twolevel system, such as a Landau-Zener sweep, can be extended to many-body quantum systems. We will focus especially on the case where the interactions and the correlations are tuned in the system. In the same experimental setup, we plan to extend the superlattice setup towards the realization of coupled plaquette systems and use these to study re-entrance phenomena in the superfluid-Mott insulator transition that have been shown to play a crucial to explain disorder induced re-entrance behaviour in disordered bosonic quantum gases.