High-order harmonic generation processes in classical and quantum anharmonic oscillators

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Abstract
We present a theoretical study of high-order harmonic generation by a slowly driven ‘‘Duffing’’ anharmonic oscillator. The power spectra are shown to display a plateau of high harmonics, which ends up with a sharp cutoff. The classical dynamics is analyzed with the adiabatic invariance theorem, which yields a simple interpretation to this characteristic behavior. We compare with the quantum case by solving numerically the time-dependent Schrödinger equation, and outline the similarity between classical damping and quantum-mechanical ionization processes. This allows us, in particular, to interpret the existence of intrinsic phases between high harmonics and the driving field. We further discuss the implication of these relaxation processes on the coherence of high harmonics, as well as the existence of interference processes yielding quasiresonant structures in intensity dependences. © 1996 The American Physical Society.