Raman transitions without adiabatic elimination: A simple and accurate treatment

TL;DR

This paper presents a new method for analyzing driven Raman processes that avoids adiabatic elimination, providing more accurate results especially when the intermediate state is not far detuned.

Contribution

The authors introduce an alternative approach that retains all states in the analysis, improving accuracy over traditional adiabatic elimination methods.

Findings

Accurate results achieved with a simple lowest-order approximation.

Method applicable when intermediate state detuning is small.

Provides a hierarchy of approximations for improved precision.

Abstract

Driven Raman processes --- nearly resonant two-photon transitions through an intermediate state that is non-resonantly coupled and does not acquire a sizeable population --- are commonly treated with a simplified description in which the intermediate state is removed by adiabatic elimination. While the adiabatic-elimination approximation is reliable when the detuning of the intermediate state is quite large, it cannot be trusted in other situations, and it does not allow one to estimate the population in the eliminated state. We introduce an alternative method that keeps all states in the description, without increasing the complexity by much. An integro-differential equation of Lippmann-Schwinger type generates a hierarchy of approximations, but very accurate results are already obtained in the lowest order.