Quantum Simulation seeks to unravel the mysteries of complex quantum systems that influence fields like materials science, chemistry, and biology. By modelling these systems through precise, controlled experiments at the quantum-mechanical level, we gain new, profound insights.

Within this PhD project, we'll utilize ultracold atoms in optical lattices in a quantum-gas microscope, capable of single-site-resolved atom detection. Our setup, equipped with spatial light modulators, can project various light patterns onto the atoms with remarkable resolution. For example, in our work, published in Nature Communications we were able to create quantum systems with only five atoms on a specific number of lattice sites.

This remarkable tool will allow us to investigate novel quantum states in quasi-one-dimensional systems. You can be the future PhD student exploring quantum states in ladder systems at half filling, where atoms move across each rung, yet the overall state remains insulating!

We're also diving into the intriguing effects of disordered lattice potentials on quantum states. By manipulating light potentials to flip atomic spins on selected sites, we'll create various initial spin distributions, shedding light on out-of-equilibrium dynamics.

And there's more - future studies will venture into complex lattice geometries like Lieb-lattice systems and diamond chains.