Abstract
In this chapter, and by analogy with Quantum Optics, the properties of SQUID rings (here, a Josephson weak link enclosed by a thick superconducting ring) in the quantum regime are discussed. In particular, the possibility of frequency down conversion is investigated, via a quantum mechanical SQUID ring, between quantised electromagnetic field oscillator modes. It is shown that because of the non-perturbative properties of the SQUID ring (essentially due to the cosinusoidal Josephson coupling term in the ring potential) multi-photon down conversion can take place between an input photon and output photons at sub-integers of the input frequency. In addition, these output photons are created in an entangled state with a degree of entanglement that could be modified through the static magnetic flux applied to the SQUID ring.
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