Effective Hamiltonians in quantum optics: a systematic approach

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.

13 Pages, no figures, submitted for publication

References in corpus (4)

• An Algebraic Approach to Solving Evolution Problems in Some Nonlinear Quantum Models
• Coherent States of Non-Linear Lie algebras: Application in Quantum Optics
• On Nonlinear Angular Momentum Theories, Their Representations and Associated Hopf Structures
• On some nonlinear extensions of the angular momentum algebra

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