Understanding strongly-interacting systems is at the frontier of modern quantum physics. These systems have an extremely large variety in energy and length scales, and range from high-Tc superconductors to the dense interiors of neutron stars. We investigate the many-body physics of such systems in a bottom up approach, starting from unifying concepts of two-, three, and few-body physics, which is quite different from usual fashion in condensed matter physics. Our model systems are based on ultracold atomic quantum gases that are experimentally easy to manipulate, and which have the indispensable ability to precisely control their interparticle interactions by tuning a magnetic field. This allows the quantum gas to reach the unitary regime, where atoms interact very strongly. We develop unifying concepts that require the introduction of finite range interactions, which we explore from short to long range. Our work is at a fundamental level, but also significant for the development of new quantum materials and quantum simulators.
Quantum simulators can be regarded as analog quantum computers, and permit the study of (novel) quantum systems that are difficult to study in the laboratory, and which are essentially impossible to solve on classical computers. A quantum simulator is designed to explore specific problems, for instance in quantum chemistry and bio-molecular physics, where there are important open questions related to energy transport in photosynthetic complexes and catalytic cycles of high biological interest. We investigate quantum simulators based on ultracold Rydberg atoms. In Rydberg atoms the outermost electron is highly excited and is only weakly bound to the atom. Thanks to these electrons the interactions between Rydberg atoms are very strong and the atoms form a good basis for a quantum bit.