Quantum phenomena in a chirped parametric anharmonic oscillator

Parametric ladder climbing and the quantum saturation of the threshold for the classical parametric autoresonance due to the zero point fluctuations at low temperatures are discussed. The probability for capture into the chirped parametric resonance is found by solving the Schrödinger equation in the energy basis and the associated resonant phase-space dynamics is illustrated via the Wigner distribution. The numerical threshold for capture into the resonance is compared with the classical and quantum theories in different parameter regimes.