The anharmonic oscillator as a Bloch–Siegert model

A model of a quantum anharmonic oscillator interacting with a classical coherent field of a single carrier frequency is considered. It is shown that the application of algebraic perturbation theory in the case of resonant interaction leads to a two-level atom model in which the Stark shift of the resonant levels differs depending on the resonant quantum transition and differs in the general case from both the Bloch–Siegert shift and the Stark shift of an ordinary multilevel atom. The constructed model allow describing coherent effects in an ensemble of anharmonic oscillators, which is shown by the example of nutation oscillations.