Dynamical bifurcation and amplification in Josephson junction oscillators

This chapter presents a theoretical and experimental overview of dynamical bifurcation in driven Josephson junction based nonlinear oscillators. Capture into one of the two driven states can be strongly influenced by a small variation of the oscillator parameters, thus giving rise to sensitive amplification. For an amplitude modulated drive current, state transitions are described by fluctuation induced activation over an energy barrier. When frequency modulation is used to access the bifurcation region, the oscillator can either phase lock to the drive signal and exhibit large oscillation amplitude or decay to the low amplitude state - a phenomenon known as autoresonance. In this out of equilibrium process, fluctuations only set the initial condition of the oscillator and do not affect its subsequent dynamics. Both models are valid in the presence of either thermal fluctuations or quantum noise, which ultimately limits the sensitivity of such amplifiers.