The nonlinear effects of noise on parametric amplification: An analysis of noise rise in Josephson junctions and other systems

We take a new look at an old problem; namely, the observed ‘‘noise rise’’ in superconducting Josephson junction parametric amplifiers. By exploiting recent insights from dynamical systems theory, we show how the interplay or random noise and (nonchaotic) deterministic dynamics can result in a noise rise like that observed in experiments. Our analysis leads to a universal first-order equation which applies to all similar systems in the high-gain regime. We propose several predictions which can be tested experimentally, including that a similar noise rise should occur in modulated semiconductor injection lasers. We also analyze a previously unknown mode of operation—a ‘‘six-photon’’ mode associated with a symmetry breaking bifurcation—and discuss its potential advantages over the previously studied three- and four-photon modes.