Two-laser multiphoton adiabatic passage in the frame of the Floquet theory. Applications to (1+1) and (2+1) STIRAP

We develop an adiabatic two-mode Floquet theory to analyse multiphoton coherent population transfer in Ai-level systems by two delayed laser pulses, which is a generalization of the three-state stimulated Raman adiabatic passage (STIRAP). The main point is that, under conditions of non-crossing and adiabaticity, the outcome and feasibility of a STIRAP process can be determined by the analysis of two features: (i) the liking of degeneracy of dressed states at the beginning and at the end of the laser pulses, and (ii) the connectivity of these degeneracy-lifted branches in the quasienergy diagram. Both features can be determined by stationnary perturbation theory in the Floquet representation. As an illustration, we study the corrections to the RWA of the (1+1) STIRAP in strong fields and for large detunings. We analyse the possible breakdown of connectivity. In strong fields, the complete transfer is achieved, but the intermediate state, unpopulated within the RWA, can become populated during the process. In the (2+1) STIRAP, we show a residual degeneracy in a four-level system, that can be liked by additional Stark shifts. The complete transfer is achieved under conditions of connectivity.