Doubly resonant ultrachirped pulses

TL;DR

This paper investigates ultrachirped pulses with large frequency chirps crossing resonance twice, revealing differences in field decompositions and showing how the analytic signal improves the validity of the rotating wave approximation.

Contribution

It introduces a detailed analysis of ultrachirped pulses crossing resonance twice and demonstrates the advantages of the analytic signal representation in quantum optical interactions.

Findings

Analytic signal representation extends the validity of the rotating wave approximation.

Resonance crossing occurs twice for large chirps, affecting field decomposition.

Differences in amplitude and phase factors depend on the field decomposition method.

Abstract

Ultrachirped pulses for which the frequency chirp is of the order of the transition frequency of a two-level atom are examined. When the chirp is large enough, the resonance may be crossed twice, for positive and negative quadrature frequencies. In this scenario the analytic signal and quadrature decompositions of the field into amplitude and phase factors turn out to be quite different. The corresponding interaction pictures are strictly equivalent, but only as long as approximations are not applied. The domain of validity of the formal rotating wave approximation is dramatically enhanced using the analytic signal representation.