Two-photon ladder climbing and transition to autoresonance in a chirped oscillator

TL;DR

This paper explores two-photon ladder climbing and autoresonance in a chirped quantum nonlinear oscillator, providing a unified quantum-classical analysis and identifying the phase-locking transition threshold through theoretical and numerical methods.

Contribution

It introduces a novel isomorphism between quantum and classical resonances, enabling calculation of phase-locking thresholds in both regimes.

Findings

Quantum and classical thresholds for phase-locking are calculated.

The theory is validated by solving the Schrödinger equation.

Wigner function analysis illustrates the quantum-classical transition.

Abstract

The two-photon ladder climbing (successive two-photon Landau-Zener-type transitions) in a chirped quantum nonlinear oscillator and its classical limit (subharmonic autoresonance) are discussed. An isomorphism between the chirped quantum-mechanical one and two-photon resonances in the system is used in calculating the threshold for the phase-locking transition in both the classical and quantum limits. The theory is tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space.