The research paper provides the classification of resonant interactions of a coherent field with an anharmonic oscillator using the established analogy with multiphoton interactions of light with atoms. In this context consideration is given to the characteristic nonlinear terms in the Hamiltonian, which change the state of the anharmonic oscillator by means of a certain number of quanta p. The interference interaction, in which the absorption of one quantum of a coherent field leads to a multiquant transition in an anharmonic oscillator due to electrodipole interaction and nonlinearity, manifests itself both as the superposition of resonances of the cascade type and the lambda-V type. Taking into account the nonlinearity of the third and fourth orders, the general formulas are applied to a resonant process of absorption of one photon and two-fold excitation of the oscillator. This resonance is a superposition of interference resonances of cascade type (nonlinear term with p=1) and lambda type (nonlinear term with p=3, see Fig.).

The resonant processes of both second harmonic and low-frequency generation of emission are predicted and described, with its experimental study of nutations allowing us to estimate the parameters of anharmonicity of the considered model. The analogy and effective resonant operators are obtained using algebraic perturbation theory, which differs from the canonical Van Fleck perturbation theory, for example, by requiring the absence of time-varying terms in the effective Hamiltonian in the Dirac picture.

Basharov A.M.
JETP Letters 120, issue 6 (2024)