Effective Hamiltonians in quantum optics: a systematic approach

2002/09/02 by A. B. Klimov, L. L. Sanchez-Soto, A. Navarro +1 · 1 citation
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1080/09500340210134675

published as J. Mod. Opt 49, 2211-2226 (2002) · 13 Pages, no figures, submitted for publication

arxiv created 2002/09/02 · arxiv updated 2009/12/01

Abstract

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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