Classical and quantum-mechanical phase-locking transition in a nonlinear oscillator driven by a chirped-frequency perturbation is discussed. Different limits are analyzed in terms of the dimensionless parameters P 1=/√2mω0α and P2=(3β)/ (4m√α) (ε, α, β, and ω0 being the driving amplitude, the frequency chirp rate, the nonlinearity parameter, and the linear frequency of the oscillator). It is shown that, for P2P 1+1, the passage through the linear resonance for P1 above a threshold yields classical autoresonance (AR) in the system, even when starting in a quantum ground state. In contrast, for P2P 1+1, the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in P1 in both AR and LC limits are calculated. The theoretical results are tested by solving the Schrödinger equation in the energy basis and illustrated via the Wigner function in phase space.
|Original language||American English|
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|State||Published - 29 Jul 2011|