Jens Koch, Northwestern University
Quantum simulators such as systems of ultracold atoms in optical lattices enable one to explore exotic quantum phases of matter and systematically study quantum phase transitions between them. Recently demonstrated photonic systems based on circuit QED (Quantum ElectroDynamics) arrays feature exciting properties that set them apart from these conventional quantum simulators. In particular, a crucial difference is the intrinsic open-system character of photon-based systems. In this talk, I will discuss the theoretical challenges in modeling large open quantum systems and in predicting possible dissipative phase transitions. To address these challenges, I will then present our work on a perturbative formalism for the Lindblad master equation, suitable for infinite systems and capable of handling self-energy corrections. Manifestly built upon a controlled approximation, we expect this approach to shed new light on the validity of numerical results and mean-field treatments.