Method of small rotations and effective Hamiltonians in nonlinear quantum optics

We propose a general method for diagonalizing a wide class of nonlinear Hamiltonians describing different quantum optical models. This method makes use of a nonlinear deformation of the usual su(2) algebra and when some physical parameter, dictated by the particular model under consideration, becomes small, it gives a diagonal effective Hamiltonian that describes correctly the dynamics for arbitrary states and long times. We apply as well the technique to three-level systems interacting with quantum fields, showing that it is possible to engineer resonant interactions through nonresonant processes.