Quantum versus classical phase-locking transition in a frequency-chirped nonlinear oscillator

Journal Article · Fri Jul 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.84.013837· OSTI ID:22058796

Barth, I; Friedland, L; Gat, O ^[1]; Shagalov, A G ^[2]

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1. Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2. Institute of Metal Physics, Ekaterinburg 620219 (Russian Federation)

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{sub 1}={epsilon}/{radical}(2m({Dirac_h}/2{pi}){omega}{sub 0}{alpha}) and P{sub 2}=(3({Dirac_h}/2{pi}){beta})/(4m{radical}({alpha})) ({epsilon}, {alpha}, {beta}, and {omega}{sub 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{sub 2}<>P{sub 1}+1, the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in P{sub 1} in both AR and LC limits are calculated. The theoretical results are tested by solving the Schroedinger equation in the energy basis and illustrated via the Wigner function in phase space.

• OSTI ID: 22058796
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 84; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FUNCTIONS
GROUND STATES
NONLINEAR PROBLEMS
OSCILLATORS
PERTURBATION THEORY
PHASE SPACE
QUANTUM MECHANICS
RESONANCE
SCHROEDINGER EQUATION