Adiabatic Floquet theory Hamiltonian

In this chapter, the main theoretical tools used in the work presented in the next two chapters on the laser control of the radiationless decay in pyrazine and of the tunneling dynamics in NHD2, are introduced. After a brief discussion of the main approximations generally made in the study of laser-molecule interactions, presented in Sect. 6.1, we introduce in Sect. 6.2 the most basic tools for the laser control of population transfer in a two-level system. The derivation of an effective Hamiltonian allowing for the description of the interaction of a molecular system with a strong non-resonant laser pulse is presented in Sect. 6.3. TheFloquet theory and the adiabatic Floquet theory are Anally introduced in Sects. 6.4 and 6.5. 

A theoretical treatment of the DREAM adiabatic homonuclear recoupling experiment has been given using Floquet theory. An effective Hamiltonian has been derived analytically and the time evolution of the density operator in the adiabatic limit has been described. Shape cycles have been proposed and characterized experimentally. Application to spin-pair filtering as a mixing period in a 2D correlation experiment has been explored and the experimental results have been compared to theoretical predictions and exact numerical simulations. 

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