Simultaneous multiphoton processes in the interaction of atoms with electromagnetic fields

It is impossible to obtain an exact description of multiphoton processes in the interaction of electromagnetic fields with atomic systems. Approximate approaches must be used to describe the physically different effects that can occur. One effect is the stepwise absorption/emission of many photons by a N-level system that evolves dynamically in between each absorption/emission. Another effect is described in the theories of Raman processes where the simultaneous absorption/emission of many photons is considered. In this paper, consideration is given to both processes allowing interference between the stepwise and simultaneous absorptions. An approximate Hamiltonian is obtained from the quantum mechanical multipole expansion. An exact solution of an atom-field system subject to this Hamiltonian will be presented. The extension of the method to multiple electromagnetic fields is discussed