Quantum versus classical phase-locking transition in a driven-chirped oscillator

Abstract

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 and $P_2=(3\hslash \beta )/(4m\sqrt{\alpha })$ ($\epsilon ,$ $\alpha ,$ $\beta$ and ${\omega }_0$ being the driving amplitude, the frequency chirp rate, the nonlinearity parameter and the linear frequency of the oscillator). It is shown that for $P_2\ll P_1+1$, the passage through the linear resonance for $P_1$ above a threshold yields classical autoresonance (AR) in the system, even when starting in a quantum ground state. In contrast, for , the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in $P_1$ in both AR and LC limits are calculated. The theoretical results are tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space.

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• Autoresonant control of the many-electron dynamics in nonparabolic quantum wells
• Switching via quantum activation: A parametrically modulated oscillator
• Critical exponents in metastable decay via quantum activation
• Phase-locking transition in a chirped superconducting Josephson resonator
• Quantum Fluctuations in the Chirped Pendulum
• Experimental Study of Parametric Autoresonance in Faraday Waves

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