Lie-type transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems

Details Lie-type transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems Lie-type transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems

2001-02-09

arxiv.org/abs/quant-ph/0102050v1

Physics

Quantum Physics

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

Scientific paper

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.

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