Quantum Simulations with Atoms and Molecules in Optical Lattices

Forty years ago, Richard Feynman outlined his vision for a quantum computer, specifically for simulating complex physical problems through quantum calculations. Today, his dream of analog and digital quantum simulations has become a reality, making it a highly active field of research across various platforms, ranging from ultracold atoms and ions to superconducting qubits and photons. In my talk, I will outline how ultracold atoms in optical lattices initiated this vibrant and interdisciplinary research field 20 years ago and now enable the probing of quantum many-body phases in- and out-of-equilibrium with fundamentally new tools, providing single-particle resolution and control. Novel (hidden) order parameters, entanglement properties, full counting statistics, or topological features can now be measured routinely, providing deep new insights into the world of correlated quantum matter. In addition to presenting ways to realize p-wave superfluids with polar fermionic molecules, I will also describe novel routes to achieve high-atom-number, low-entropy phases for ultracold fermions in optical lattices and present measurements on universal correlation properties in the pseudogap phase of the Fermi-Hubbard model.