Lie-type transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems
نویسندگان
چکیده
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. PACS number(s): 03.65.Bz, 03.65.Ca, 42.50.Hz, 42.50.Fx
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