Dynamics of correlated many-body quantum systems

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Quantum Simulation seeks to gain fundamental insight into the behaviour of complex microscopic systems, which underlie diverse fields ranging from materials science to chemistry and biology. New understanding can now be achieved by modelling (or simulating) this behaviour with experiments that are controllable on a microscopic, quantum-mechanical level. This provides a revolutionary approach that could solve problems that are currently intractable for even the fastest supercomputer.Ultracold atoms in optical lattices offer the unique possibility to study such behaviour of many-body quantum systems in our laboratories. In particular, we have setup quantum-gas microscope platforms, which have enabled us to achieve single-site and single-atom resolved detection of atoms in an optical lattice. This exciting new tool will open the path to the study of strongly correlated fermionic quantum systems in optical lattices with unprecedented insight into their local properties, which is the core subject of the project. *Quantum spin models. The first part of the of the project will be devoted to improve the single-atom imaging systems and implement the laser cooling of a second atomic species to realise two-component ultracold quantum gases in an optical lattice. Such a system of two-component bosonic atoms can mimic different spin models, which are of importance in condensed matter physics. The tailorable scattering lengths will make it possible to implement S=1/2 and S=1 models with (near) Heisenberg symmetry. We can also engineer, antiferromagnetic exchange by control over the interactions within one species, so that this interaction strength becomes markedly different to the other scales of interaction strength in the system: Another way of doing so is by preparation of the system into a highly excited initial state generated by the sudden imposition of staggered onsite energies such that the Mott insulator is a metastable state, and exchange energies change sign. A further technique which may be tested are Floquet modulation techniques. *Quench dynamics with bosonic atoms. A key goal is to study the out-of-equilibrium dynamics of many-body fermionic quantum systems. We are planning to extend the previous studies of correlation dynamics in 1D to uniform 2D systems, where existing numerical and analytical approaches suffer from limitations. We are planning for example create a charge-density wave using tailored light potentials and observe its relaxation to equilibrium, and we will in particular study the dynamics as a function of the interspecies interaction. Single or multi-site addressing will also allow us to perform local quenches. Single-atom imaging will enable us to monitor the direct spreading of correlations in many-body systems not only in one dimension but also in 2D or in different lattice geometries, such as triangular lattices. Furthermore, the production rate of excitations and the formation of magnetic domains when tuning the effective interaction strength slowly across the critical point can be directly imaged in-situ to explore Kibble-Zurek-like physics.