  When connecting a voltage-biased Josephson junction in series to several
microwave cavities, a Cooper-pair current across the junction gives rise to a
continuous emission of strongly correlated photons into the cavity modes.
Tuning the bias voltage to the resonance where a single Cooper pair provides
the energy to create an additional photon in each of the cavities, we
demonstrate the entangling nature of these creation processes by simple
witnesses in terms of experimentally accessible observables. To characterize
the entanglement properties of the such created quantum states of light to the
fullest possible extent, we then proceed to more elaborate entanglement
criteria based on the knowledge of the full density matrix and provide a
detailed study of bi- and multipartite entanglement. In particular, we
illustrate how due to the relatively simple design of these circuits changes of
experimental parameters allow one to access a wide variety of entangled states
differing, e.g., in the number of entangled parties or the dimension of state
space. Such devices, besides their promising potential to act as a highly
versatile source of entangled quantum microwaves, may thus represent an
excellent natural testbed for classification and quantification schemes
developed in quantum information theory.
