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A quantum system comprising of a monochromatic electromagnetic field coupledto a SQUID ring with sinusoidal non-linearity, is studied. A magnetostatic flux$\Phi_{x}$ is also threading the SQUID ring, and is used to control thecoupling between the two systems. It is shown that for special values of$\Phi_{x}$ the system is strongly coupled. The time evolution of the system isstudied. It is shown that exchange of energy takes place between the two modesand that the system becomes entangled. A second quasi-classical model thattreats the electromagnetic field classically is also studied. A comparisonbetween the fully quantum mechanical model with the electromagnetic fieldinitially in a coherent state and the quasi-classical model, is made.

Fully quantum-mechanical model of a SQUID ring coupled to an electromagnetic field