Lietype transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 February 2001
 arXiv:
 arXiv:quantph/0102050
 Bibcode:
 2001quant.ph..2050K
 Keywords:

 Quantum Physics
 EPrint:
 12 pages, no figures Proceedings of XXIII International Conference on Group Theoretical methods in Physics, Dubna 2000