A Investigation of the Factorization of the Third - One-Time Correlation Function for Three Related Model Potentials

The factorization of the third-order one-time correlation function is investigated for a quartic anharmonic oscillator, a diagonal approximation to a quartic anharmonic Hamiltonian, and a Lorentzian potential. It is shown that when laser driving is near the ground-state resonance, the factored correlation function is similar to the unfactored correlation function for all three potentials. When the driving field becomes strong or the frequency of the driving laser field is detuned significantly from the ground-state resonance, the Lorentzian potential is the most stable.