Different techniques to speed up quantum adiabatic processes are currently being explored for applications in atomic, molecular and optical physics, such as transport, cooling and expansions, wavepacket splitting, or internal state control. Here we e
xamine the capabilities of superadiabatic iterations to produce a sequence of shortcuts to adiabaticity. The general formalism is worked out as well as examples for population inversion in a two-level system.
A Schrodinger equation may be transformed by unitary operators into dynamical equations in different interaction pictures which share with it a common physical frame, i.e., the same underlying interactions, processes and dynamics. In contrast to this
standard scenario, other relations are also possible, such as a common interaction-picture dynamical equation corresponding to several Schrodinger equations that represent different physics. This may enable us to design alternative and feasible experimental routes for operations that are a priori difficult or impossible to perform. The power of this concept is exemplified by engineering Hamiltonians that improve the performance or make realizable several shortcuts to adiabaticity.
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.
