Adiabatic Floquet theory pulses

In the following section the experimental approach is briefly described. The initial observations of microwave ionization and the completely non-resonant picture initially used to describe it are then presented. Then microwave multiphoton transitions in a two level system analogous to the rate limiting step of microwave ionization are described both experimentally and theoretically. Experiments on this two level system with well controlled pulses of microwaves to show the applicability of an adiabatic Floquet theory to pulses are then described. We finally return to microwave ionization to see evidence for the resonant nature of the process. 

CONTROL OF QUANTUM DYNAMICS BY LASER PULSES ADIABATIC FLOQUET THEORY... 

S. Guerin, H.R. Jauslin, Control ofquantom dynamics by laser pulses Adiabatic Floquet theory, Adv. Chem. Phys. 125 (2003) 147. 

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. 

Guerin S, Jauslin HR (2003) Control of quantum dynamics by laser pulses adiabatic floquet theory. Adv Chem Phys 125 147-267... 

At the resonance w(t) = A(x), the adiabatic potentials i.e. the eigenvalues of (5.9) show avoided crossing and the population splits into the two adiabatic Floquet states. In the case of quadratically chirped pulses, the instantaneous frequency meets the resonance condition twice and near-complete excitation can be achieved due to the constructive interference. The nonadi-abatic transition matrix Ujj for the two-level problem of (5.9) is given by the ZN theory [33] as... 

Thus, Floquet theory provides a natural means of studying the dynamics of the response of an atomic system to a pulsed laser field. Indeed, it yields a general framwork for discussing the adiabatic motion of any periodically driven quantum system. If we define a characteristic time St = 6A/(dA/dt) which is the time taken to sweep through the avoided crossing, then one can distinguish between three regimes ... 

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