Lie-type transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems
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We reelaborate on 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 extend the technique to $N$-level atomic systems interacting with quantum fields, finding the corresponding effective Hamiltonians when the condition of $k$-photon resonance is fulfilled.
12 pages, no figures Proceedings of XXIII International Conference on Group Theoretical methods in Physics, Dubna 2000
12 pages, no figures Proceedings of XXIII International Conference on Group Theoretical methods in Physics, Dubna 2000