Quantum simulation with ultracold atoms*

Numerical calculations of quantum many-body systems scale in general exponentially with the number of quantum particles. Larger systems, in particular in the transition to the thermodynamic limit, represents a big challenge and are often not tractable with classical algorithms. Quantum simulation offers a path to more insight for larger systems by realizing the Hamiltonian of interest directly. Here I will discuss approaches using ultracold atoms in optical potentials to perform quantum simulation of Hubbard models and quantum spin systems. In the lab, it is nowadays possible to realize arrays of several thousand atoms with individual control and detection of every atom. The two most prominent atomic platforms with single atom detection are quantum gas microscopes, which are based on ultracold atoms loaded into optical lattices with tunnel coupling, and optical tweezer arrays, where every atom is individually trapped using an optical tweezer. I will discuss both approaches and give an outlook on new possibilities arising by combining ideas of both platforms.