Effective Hamiltonians in quantum optics: a systematic approach

Details Effective Hamiltonians in quantum optics: a systematic approach Effective Hamiltonians in quantum optics: a systematic approach

2002-09-02

arxiv.org/abs/quant-ph/0209013v1

J. Mod. Opt 49, 2211-2226 (2002)

Physics

Quantum Physics

13 Pages, no figures, submitted for publication

Scientific paper

10.1080/09500340210134675

We discuss a general and systematic method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the dynamical symmetry of the original model. When some physical parameter, dictated by the process under consideration, becomes small, we immediately get a diagonal effective Hamiltonian that correctly represents the dynamics for arbitrary states and long times. We extend the technique to su(3) and su(N), finding the corresponding effective Hamiltonians when some resonance conditions are fulfilled.

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