Embedding a Josephson junction within a superconducting microwave cavity provides a novel way of exploring strongly non-linear quantum dynamics. Energy from a flow of Cooper pairs through the Josephson junction (driven by an applied  voltage) pumps the cavity generating a large population of photons which in turn strongly affect the charge dynamics. This results in interesting non-equilibrium steady-states in the cavity which can have a range of non-classical properties. In this talk I will outline a simple theoretical model inspired by recent experimental work on Josephson junction-cavity systems and describe the coupled dynamics of the cavity photons and Cooper pairs. 

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