Floquet theory for short laser pulses

We develop adiabatic perturbation theory for quantum systems responding to short laser pulses, with or without a frequency chirp. Our approach rests on lifting the time-dependent Schrodinger equation to an extended Hilbert space, then applying standard perturbational techniques to Floquet states in this extended space, and finally projecting back to the physical Hilbert space. The same strategy also allows us to construct superadiabatic bases for monitoring the quantum evolution in the course of a pulse. These bases provide a diagnostic tool for improving the efficiency of pulse-induced population transfer. The formalism is: applied to the selective excitation of molecular vibrational states by chirped laser pulses, which exploit either successive single-photon resonances or a multiphoton resonance; and by a STIRAP-like process.