Classical and Quantum Autoresonant Transition

Autoresonance (AR) 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 AR exist in atomic and molecular physics, plasmas, fluids, nonlinear optics, planetary dynamics, and Josephson junctions. The salient feature of AR is the existence of a sharp threshold on the amplitude of the oscillating, chirped frequency driving perturbation for transition to AR.  In this talk, I will address the influence of classical and quantum fluctuations on the AR phaselocking transition and the bunching effect due to self fields. 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 3/4α (α being the chirp rate) and ( )1/2αT , respectively [1]. Strong repulsive self-fields reduce the width of the threshold considerably, as the ensemble forms a localized autoresonant macro-particle [1]. This result was an essential part of the mixing scheme in anti-hydrogen formation experiment at CERN. Due to quantum fluctuations, T should be replaced by an effective temperature,Teff, where T T eff = in the classical regime and 0/ 2Bℏω kin 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]. Finally, I will address the quantum counterpart of the classical AR phenomenon, i.e., the quantum ladder climbing, and the continuous transition between these two regimes [3]. [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, and I. Siddiqi1, Nature Physics 7, 105 (2011).  [3] I. Barth, L. Friedland, O. Gat, and A.G. Shagalov, Phys. Rev. A 84, 013837 (2011).