Quantum versus classical phase-locking transition in a frequency-chirped nonlinear oscillator
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
- 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, Vol. 84, Issue 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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