2006/11/30 by Martin Kiffner, M. Kiffner, Jörg Evers +3
Computer Science · Mathematics · Physics and Astronomy · #Angular momentum #Atom (system on chip) #Atomic physics #Cold Atom Physics and Bose-Einstein Condensates #Degenerate energy levels #Dipole #Electric dipole transition #Geometry #Magnetic dipole #Mathematics #Orientation (vector space) #Physics #Quantum Information and Cryptography #Quantum electrodynamics #Quantum mechanics #Quantum optics and atomic interactions #Spin (aerodynamics) #Zeeman effect #quant-ph
paper · pdf · doi:10.1103/physreva.76.013807
published as Phys. Rev. A 76, 013807 (2007)
arxiv created 2007/06/04 · openalex publication_date 2007/07/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The validity of the few-level approximation in dipole-dipole interacting collective systems is discussed. As an example system, we study the archetype case of two dipole-dipole interacting atoms, each modeled 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.