Quantum phenomena in a chirped parametric anharmonic oscillator

Abstract

The parametric ladder climbing (successive Landau-Zener-type transitions) 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 Schrodinger equation in the energy basis and the associated resonant phase space dynamics is illustrated via the Wigner distribution. The numerical threshold for the efficient capture into the resonance is compared with the classical and quantum theories in different parameter regimes.

5 pages, 3 figures

References in corpus (6)

• Charge insensitive qubit design derived from the Cooper pair box
• Autoresonant control of the many-electron dynamics in nonparabolic quantum wells
• Parametric Resonance of Optically Trapped Aerosols
• Phase-locking transition in a chirped superconducting Josephson resonator
• Classical to quantum transition of a driven nonlinear nanomechanical resonator
• Experimental Study of Parametric Autoresonance in Faraday Waves

Cited by in corpus (9)

• Kinetic simulations of ladder climbing by electron plasma waves
• On the effect of beating during nonlinear frequency chirping
• Capture into resonance and phase space dynamics in optical centrifuge
• Ladder Climbing and Autoresonant Acceleration of Plasma Waves
• Bifurcations of autoresonant modes in oscillating systems with combined excitation
• Nonlinear optomechanical resonance entering a self-organized energy transfer pattern
• Capture into parametric autoresonance in the presence of noise
• Missing Rung Problem in Vibrational Ladder Climbing
• Autoresonant Removal of Fusion Products in Mirror Machines