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Far-off-resonant pulsed laser fields produce negligible excitation betweentwo atomic states but may induce considerable phase shifts. The acquired phasesare usually calculated by using the adiabatic-elimination approximation. Weanalyze the accuracy of this approximation and derive the conditions for itsapplicability to the calculation of the phases. We account for various sourcesof imperfections, ranging from higher terms in the adiabatic-eliminationexpansion and irreversible population loss to couplings to additional states.We find that, as far as the phase shifts are concerned, the adiabaticelimination is accurate only for a very large detuning. We show that theadiabatic approximation is a far more accurate method for evaluating the phaseshifts, with a vast domain of validity; the accuracy is further enhanced bysuperadiabatic corrections, which reduce the error well below $10^{-4}$.Moreover, owing to the effect of adiabatic population return, the adiabatic andsuperadiabatic approximations allow one to calculate the phase shifts even fora moderately large detuning, and even when the peak Rabi frequency is largerthan the detuning; in these regimes the adiabatic elimination is completelyinapplicable. We also derive several exact expressions for the phases usingexactly soluble two-state and three-state analytical models.

Phase shifts in nonresonant coherent excitation