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

A. B. Klimov·A. Navarro·L. L. Sanchez-Soto
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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.

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A. B. Klimov, A. Navarro, L. L. Sanchez-Soto. 2001-02-09. Lie-type transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems. https://arxiv.org/abs/quant-ph/0102050

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