Adiabatic chirping of the driving frequency is a powerful method for controllable excitation of a quantum state in an anharmonic oscillator. When the driving amplitude exceeds a threshold, this novel approach yields a continuous climbing the quantum energy ladder of the oscillator [1]. The threshold for this excitation process is calculated by analyzing successive Landau-Zener transitions in the system. The classical limit of the dynamics, where many levels are coupled simultaneously is addressed, introducing the classical counterpart of the quantum ladder climbing, i.e. the classical autoresonance. The Wigner representation of the system is used to illustrate the quantum-classical transition, as well as the evolution of the resulting phase-locked quasi-coherent state of the driven nonlinear oscillator.

[1] I. Barth, L. Friedland, O. Gat, and A.G. Shagalov, Phys. Rev. A 84, 013837 (2011).