Dynamics of many-photon excitation of molecular vibrations

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 p_n(ω _l, t) of a level n is studied in the case when the field broadening is weak compared with the anharmonicity. The population p_n, 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 p_n and the time taken to reach this value. The value of p_n 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 p_n 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.