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 t
his 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.
We study the scaling and coordinate transformation to physically simulate quantum three-body collinear chemical reactions of the type A+BC $rightarrow$ AB+C by the motion of single ultracold atoms or a weakly interacting Bose-Einstein condensate on a
n $L$-shaped waveguide. As an example we show that the parameters to model the reaction F+HH $to$ H+HF with lithium are at reach with current technology. This mapping provides also an inverse scattering tool to find an unknown potential, and a way to transfer the knowledge on molecular reaction dynamics to design beam splitters for cold atoms with control of the channel outcome and vibrational excitation.
