Quantum versus classical chirps in a Rydberg atom

The interplay between quantum-mechanical and classical evolutions in a chirped driven Rydberg atom is discussed. It is shown that the system allows two continuing resonant excitation mechanisms, i.e., a successive two-level transitions (ladder climbing) and a continuing classical-like nonlinear phase locking (autoresonance). The persistent 1:1 and 2:1 resonances between the driving and the Keplerian frequencies are studied in detail and characterized in terms of two dimensionless parameters P_1,2 representing the driving strength and the nonlinearity in the problem, respectively. The quantum-mechanical rotating wave and the classical single resonance approximations are used to describe the regimes of efficient classical or quantum-mechanical excitation in this two-parameter space.