Understanding the equilibrium and non-equilibrium dynamics of an interacting quantum system lies at the heart of many-body physics. How a closed system transits from an initial out-of-equilibrium state to a final equilibrium state is not yet clearly understood. The ability to design, control and probe such states pave the way towards understanding local and global properties of non-equilibrium dynamics. Ultracold quantum gases offer unique possibilities to study such non-equilibrium quantum dynamics in a highly controllable and precisely tunable setup.
In the first part of my talk, I will present the measurement of finite range phase coherence in an optical lattice using Talbot interferometry . Weapplied this interferometer to study the build-up of phase coherence after a quantum quench of a 87Rb Bose-Einstein condensate (BEC) residing in a one dimensional optical lattice. During the last decade ultracold fermionic alkaline-earth quantum gases have attracted a lot of attention due to their unique properties such as long lived metastable states, an ultra-narrow optical clock transition and SU(N) symmetric interactions. I will present preliminary results from our study of dissipative Fermi-Hubbard model using a 173Yb Fermi gas in a 3D magic wavelength optical lattice. I will also present our progress on setting up a state dependent optical lattice for the quantum simulation of the Kondo lattice model. Finally, I will present my ideas for the construction of a possible future quantum simulator based on ultracold lithium atoms in optical lattices.
 B. Santra, C. Baals, R. Labouvie, A. Bhattacherjee, A. Pelster, H. Ott,Nat. Commun. 8, 15601 (2017)