A treatise on the interaction of molecular systems with short-pulsed highly-intense external fields

In this review, we consider two gauges: one, the field-free gauge, is formed by the field-free electronic eigenstates and the other, the field-dressed gauge, is formed by the field-dressed electronic basis set. The field-free gauge is used, of course, in the case of time-independent systems but then it is also the more common one to be used in the case of molecular systems exposed to external fields. This gauge is conceptually simple and therefore numerically friendly — two features which make it versatile for numerical application. The field-dressed gauge is, eventually, more involved but yields deeper insight which might lead to a better understanding of the complicated interaction between a molecular system and external fields. In addition, these features can be exploited to develop efficient and reliable approximations that may save CPU (computer processing unit) time in numerical applications. These two gauges are the main topics of the present review. he general derivation of the two gauges is completed, two additional issues are discussed: (i) we extend these gauges to include external fields formed by non-classical photon-state distributions (also known as non-coherent Fock-state distributions). These photon state distributions, recently considered for the first time for molecular systems [A.K. Paul, S. Adhikari, M. Baer, R. Baer, Phys. Rev. A 81 (2010) 013412], are interesting on their own footing. Although here they mainly serve as a vehicle to test the above-mentioned novel approximations, we also devote part of the review to studying the importance of non-coherent Fock states for obtaining an unbiased correct understanding of the interaction of molecular systems with strong, short-pulsed laser fields. For this purpose, we study the photo-dissociation process of H 2 + and show (a) that the approximations, recently introduced, diminish the CPU time by about one order of magnitude with minimal loss of accuracy and (b) indeed non-coherent Fock states are found to affect molecular systems in a unique way. (ii) As mentioned, the field-dressed gauge contributes to the understanding of effects due to external fields. In the present review, we analyze the interplay between the electronic non-adiabatic coupling terms and these external interactions. This analysis relates directly to the open question whether external fields are capable of eliminating (or creating) conical intersections.