Dynamics in multicomponent systems

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This project focuses on the time-dependent density-matrix renormalization group method to simulate the dynamics of strongly correlated one-dimensional ultracold bosonic and fermionic quantum gases in optical lattices with a special emphasis on multicomponent systems. We will pursue our investigations of the use of superlattices loaded with two-species bosonic systems to observe magnetic dynamics far from equilibrium in superlattices as well as the generation of desired equilibrium states by adiabatic state preparation. In similar multispecies bosonic systems, we will investigate the dynamics of bosonic spinor condensates undergoing changes in the lattice structure (hexagonal vs. triagonal) and spin-state dependent potentials.We will also consider single-component bosonic systems with interesting out-of-equilibrium or relaxation physics: the focus will be on the relaxation in special pattern-loaded bosonic one-dimensional chains and the quantum many-body Landau-Zener effect in coupled bosonic ladders. Whereas the former is a well-controlled toy model for relaxation in a non-trivial closed quantum system, the latter is a similarly well-controlled model for adiabatic state transformations in quantum many-body systems.In fermionic systems, we will be focussing on the FFLO physics (stability, expansion dynamics) both in spin-imbalanced and mass- and spin-imbalanced systems. We will carry out extensive studies on the expansion of 1D fermionic systems after switching off the confining trap and analyze the emergence of no, ballistic or diffusive transport depending on the original quantum phase (in particular in disordered systems, where localization phenomena are expected upon release), the integrability of the model, and generally investigate the potential of this expansion method for the characterization of quantum many-body states.On the methodological side, we will be investigating new proposals to extend the reach of time-dependent DMRG to longer time-scales, mainly by switching to a Heisenberg picture, to get a better understanding of typical relaxation problems on long time scales and extract analytical relations for relaxation in interacting quantum-many body systems. This will be related to general conceptual studies of the link between high fidelity for desired states vs. high fidelity in desired observables in finite systems: the requirements for the latter will be systematically less stringent experimentally.