English

Effective Hamiltonians in quantum optics: a systematic approach

Quantum Physics 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.quant-ph/0209013,
  title  = {Effective Hamiltonians in quantum optics: a systematic approach},
  author = {A. B. Klimov and L. L. Sanchez-Soto and A. Navarro and E. C. Yustas},
  journal= {arXiv preprint arXiv:quant-ph/0209013},
  year   = {2007}
}

Comments

13 Pages, no figures, submitted for publication