Breakdown of the few-level approximation in collective systems

Details Breakdown of the few-level approximation in collective systems Breakdown of the few-level approximation in collective systems

2006-11-07

arxiv.org/abs/quant-ph/0611071v2

Phys. Rev. A 76, 013807 (2007)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.76.013807

The validity of the few-level approximation in dipole-dipole interacting collective systems is discussed. As example system, we study the archetype case of two dipole-dipole interacting atoms, each modelled by two complete sets of angular momentum multiplets. We establish the breakdown of the few-level approximation by first proving the intuitive result that the dipole-dipole induced energy shifts between collective two-atom states depend on the length of the vector connecting the atoms, but not on its orientation, if complete and degenerate multiplets are considered. A careful analysis of our findings reveals that the simplification of the atomic level scheme by artificially omitting Zeeman sublevels in a few-level approximation generally leads to incorrect predictions. We find that this breakdown can be traced back to the dipole-dipole coupling of transitions with orthogonal dipole moments. Our interpretation enables us to identify special geometries in which partial few-level approximations to two- or three-level systems are valid.

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