Forbidden bifurcations and parametric amplification in a Josephson-junction array

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Abstract
We test a general theory of parametric amplification by globally coupled arrays via numerical simulations of a shunted Josephson-junction series array operated in the three-photon mode. We find good agreement in a number of particulars: optimal amplification of periodic signals occurs near the onset of symmetry-preserving bifurcations, and gain curves follow characteristic scaling laws. We also uncover an unexpected result: the resistively shunted Josephson-junction array cannot undergo the desired bifurcation; nevertheless, substantial amplification is still possible. The response of disordered arrays is also considered.