Quantum simulations with fermionic ultracold atoms in optical lattices

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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, a quantum gas microscope has enabled us to achieve single-site and single-atom resolved detection of fermions 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.The following specific objectives will be addressed during the project: - Setup and characterisation of a spatial light modulator: the manipulation of atoms using laser field requires a very precise control of light potentials in both time and space. We plan to use a phase modulating spatial light modulator (SLM) to create holographic patterns at the position of the atoms. Project work comprises the setup of the SLM including all laser systems and corresponding optics in an independent setup aiming at the creation of light potentials optimised towards the desired properties, such as high contrast and spatial homogeneity.- Out-of equilibrium dynamics: A key scientific goal is to study the out-of-equilibrium dynamics of many-body fermionic quantum systems. The tailor-made light fields created by spatial light modulators will introduce local perturbations to the system, and the goal is to resolve and understand the ensuing dynamical evolution. A vast range of phenomena can be investigated, such as transport phenomena, quasiparticle propagation after quenches or spin-charge separation in a 1D system, as predicted within the theory of Luttinger liquids, which would be observable with the high resolution imaging system. - Novel techniques towards low-entropy quantum phases: Dynamically varying light potentials could also be used to implement schemes to deterministically remove high-entropy regions from the trap. In a theoretically proposed cooling scheme, it is suggested to cool fermions by separating regions of low and high-entropy in the lattice. The potential in the centre of the lattice is first lowered to a dimple to create a low-entropy (band insulator) phase. The high-entropy edges (metallic phase) are then pushed away or removed by selective addressing, thanks to the differential light shifts between the dimple and the edges. The dimple is adiabatically removed to reach a low-entropy phase with half-filling.