Abstract
An analysis is made of the dynamics of coherent excitation, by a resonant force, of a nonlinear quantum oscillator with an arbitrary type of anharmonicity. The behavior of the population pn(ω l, t) of a level n is studied in the case when the field broadening is weak compared with the anharmonicity. The population pn, considered as a function of the external force frequency ω l, exhibits a large number [n(n+1)] of peaks corresponding to many-photon resonances. A calculation is made of the resonance frequency of each peak and also of the maximum attainable (in the resonance under discussion) value of pn and the time taken to reach this value. The value of pn reaches unity for resonance of the levels 0 and n, no matter how weak the external field is. It is shown that in the off-resonance case the population pn may be many orders of magnitude higher than the values given by the published expressions. The application of the proposed theory to the laser-induced dissociation of polyatomic molecules is discussed.
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