Autoresonance is a salient property of many driven nonlinear systems to stay in resonance when the system's parameters vary in space and/or time. The idea was used in relativistic particle accelerators since 1946, but only 45 years later recognized as extremely important in many other fields of physics. Presently, applications of autoresonance exist in atomic and molecular physics, plasmas, fluids, acoustics, nonlinear optics, planetary dynamics, and Josephson junctions. The salient feature of autoresonance is the existence of a sharp threshold on the amplitude of the oscillating, chirped frequency driving perturbation for transition to autoresonance.

It will be shown that at small temperatures T, the capture probability versus driving amplitude is a smoothed step function with the step location and width scaling as α^3/4 (α being the chirp rate) and (αT)^1/2 , respectively [1]. Strong repulsive self-fields reduce the width of the threshold considerably, as the ensemble forms a localized autoresonant macroparticle [1]. Due to quantum fluctuations, T should be replaced by an effective temperature, T_eff , where T_eff = T  in the classical regime and hω₀/2k_B  in the quantum regime. This prediction was recently confirmed by experiments at UC Berkeley, showing quantum saturation of the width of the phase-locking transition in superconducting Josephson junctions at sufficiently low temperatures [2]. This saturation sets the absolute resolution limit of a measurement based on the autoresonance phenomenon.

[1] I. Barth, L. Friedland, E. Sarid, and A. G. Shagalov, PRL 103, 155001 (2009).

[2] K. W. Murch, R. Vijay, I. Barth, O. Naaman1, J. Aumentado, L. Friedland, I. Siddiqi1, arXiv 1008.4411v1 (2010). Accepted for publication in Nature Physics.