集体系统中少能级近似的崩溃
Breakdown of the few-level approximation in collective systems
摘要：
讨论了偶极-偶极相互作用集体系统中少能级近似的有效性。作为例子系统，我们研究了两个偶极-偶极相互作用原子的原型情况，每个原子由两套完整的角动量多重态模型化。我们建立了故障的少能级近似首先证明了直观的结果，即集体两原子状态之间的偶极-偶极诱导的能量转移取决于连接原子的矢量的长度，但不是它的方向，如果考虑完整和简并多重态。仔细分析我们的研究结果表明，简化的原子能级方案，人为地省略塞曼子级在几个级别的近似通常会导致不正确的预测。我们发现，这种故障可以追溯到偶极偶极耦合的过渡与正交的偶极矩。我们的解释，使我们能够确定特殊的几何形状，其中部分几级近似的两个或三个级别的系统是有效的。
英文摘要：
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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