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This lecture explores the field of cavity quantum electrodynamics (QED) with quantum gases, focusing on the recent developments and current status. It covers topics such as atomic self-ordering, fundamental solid-state Hamiltonians simulation, non-equilibrium many-body phenomena, and the implementation of Hubbard-like models. The lecture also discusses the emergence of dynamic gauge potentials, non-equilibrium topological phases, and the experimental observation of various phenomena like supersolidity, density and spin self-ordering, and dynamic spin-orbit coupling.
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