Ultracold atomic gases in optical cavities

Ultracold atoms coupled to electromagnetic modes of optical cavities are an exciting frontier of synthetic many-body systems that has become a reality in the laboratory. One example is the recent observation of a superradiant superfluid-to-Mott-insulator transition where cavity fields mediate forces between atoms over long distances which then compete with short-range interactions. This result has opened new opportunities for the quantum simulation of strongly-correlated many-body systems. What is more, due to decay and driving of the cavity mode, the system is far from thermal equilibrium so that dissipation and coherent dynamics can lead to non-equilibrium phase transitions. On top of that, continuous measurement of the cavity allows for in-situ observation of quantum many-body dynamics conditioned on the measurement record. In this project, we will explore scenarios relevant to experiments in the group of Esslinger (Zurich) and Hemmerich (Hamburg) as well as Thompson (Boulder) and Stamper-Kurn (Berkeley).