Phase shifts in nonresonant coherent excitation

TL;DR

This paper evaluates the accuracy of adiabatic and superadiabatic approximations in calculating phase shifts induced by far-off-resonant laser fields, highlighting their validity domains and deriving exact phase expressions.

Contribution

It provides a detailed analysis of the conditions under which adiabatic elimination accurately predicts phase shifts, including the development of superadiabatic corrections and exact phase formulas.

Findings

Adiabatic elimination is accurate only for very large detuning.

Superadiabatic corrections significantly improve phase calculation accuracy.

Exact phase expressions are derived for simplified models.

Abstract

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