Classical versus quantum harmonic-generation spectrum of a driven anharmonic oscillator in the high-frequency regime

Abstract

The harmonic-generation spectrum of an anharmonic oscillator perturbed by a high-frequency, highintensity external field is discussed from both classical and quantum mechanical points of view. The classical theory of harmonic generation in this regime is shown to provide a simple analytical expression for the probability to emit the kth harmonic of the external field frequency. The theory is applied to the harmonic generation by a charged particle moving in Morse and ‘‘soft-core’’ Coulomb model potentials and interacting with a time-periodic electric field. For both models the probability to emit the kth harmonic attains a maximal value at some k max so that a single harmonic peak dominates the spectrum. k max can be controlled by properly choosing the field and oscillator parameters. The quantum mechanical numerical results are shown to be in excellent agreement with the classical predictions due to the localization of the wave function around either stable ~in the case of Morse potential! or unstable ~in the case of ‘‘soft-core’’ Coulomb potential ! equilibrium position of the corresponding effective Kramers-Henneberger potential. @S1050-2947~98!04202-4# Atoms being irradiated by strong ac fields emit odd harmonics of the incident radiation frequency. This phenomenon, called harmonic generation ~HG!, has recently attracted a lot of attention from both experimentalists and theorists. The probability s k to emit the kth harmonic is associated with the Fourier transform of the dipole moment acceleration: