Quantum phenomena in a chirped unharmonic oscillator

Autoresonance is a fascinating phenomenon of nonlinear physics, where a perturbed nonlinear system is captured into resonance and stays phase-locked with perturbing oscillations (or waves) continuously despite variation of system's parameters. The persistent phase-locking means excursion in system's solutions space and frequent emergence of nontrivial coherent structures. For nearly half a century (starting from Veksler and McMillan in 1945) studies of autoresonance were limited to relativistic particle accelerators and microwave sources, but many new applications of the autoresonance idea emerged since 1990 in atomic physics, nonlinear dynamics, nonlinear waves, plasmas, fluid dynamics, and, most recently, superconducting Josephson junctions. 

The salient feature of autoresonance is the existence of a sharp threshold on the amplitude of the chirped frequency driving perturbation for autoresonant transition. In this talk I will discuss the effects of thermal noise and quantum fluctuations on the threshold. I will also address the quantum counterpart of the of the classical autoresonance phenomenon, i.e. the quantum ladder climbing and the continuous transition between these two regimes.