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- W1988587827 abstract "The multiple-linear-time-scale method is used to construct a perturbation theory for $N$-level quantum systems subjected to time-dependent perturbations. The secular and small-denominator terms which plague conventional time-dependent perturbation theory are avoided; consequently, the theory is useful for treating long-term behavior and resonant interactions. The introduction of a self-energy operator allows the shifts in energy levels to be displayed explicitly. When the perturbation is the dipole interaction with an electromagnetic field, the successive approximations yield the well-known rotating-wave approximation, corrections due to counter rotating terms, and the Bloch-Siegert frequency shift. The formalism is applicable to arbitrary pulse shapes, provided that $ensuremath{parallel}{H}_{1}ensuremath{parallel}ensuremath{ll}ensuremath{hbar}overline{ensuremath{omega}}$, where $ensuremath{parallel}{H}_{1}ensuremath{parallel}$ represents the inter-action strength and $overline{ensuremath{omega}}$ is a characteristic frequency of the field. Rabi oscillations induced by multiphoton resonances are automatically included, and this effect is demonstrated in the case of a square pulse with frequency approximately one half the resonance frequency for a transition between two vibrational levels of a molecule. These calculations are compared to an exact numerical solution in order to find the limits of validity of the approximation. Even at high intensities ($Iensuremath{sim}{10}^{14}$ W/${mathrm{cm}}^{2}$) the shifted resonance frequency is quite accurate; however, the approximate and exact solutions are slightly out of phase, so that the approximate solution can only be trusted for a few Rabi cycles. For much lower intensities ($Iensuremath{sim}{10}^{10}$ W/${mathrm{cm}}^{2}$), the approximate solution is valid for many thousands of Rabi cycles." @default.
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- W1988587827 date "1976-02-01" @default.
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- W1988587827 title "Multiple-time-scale perturbation theory applied to laser excitation of atoms and molecules" @default.
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- W1988587827 doi "https://doi.org/10.1103/physreva.13.674" @default.
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