磁场中耦合分子转子的成对本征态和相互排列
Pair-eigenstates and mutual alignment of coupled molecular rotors in a magnetic field
摘要：
我们研究了一对极性$^2Σ$分子在均匀磁场中的转动状态。分子之间的电偶极-偶极相互作用产生两种类型的纠缠对本征态。在一种类型中，固有顺磁性分子与磁场之间的塞曼相互作用破坏了本征态对的纠缠，而在另一种类型中则不会。成对本征态表现出许多交叉点，对于由满足电偶极-偶极算符施加的选择规则$ΔJ_{i}=0,\pm 1$、$ΔN_{i}=0,\pm 2$和$ΔM_{i}=0,\pm 1$的个体状态组成的成对本征态，这些交叉点变得避免。这里，$J_{i}$、$N_{i}$和$M_{i}$是不存在电偶极-偶极相互作用时分子$i=1,2$的总的、旋转的和投影的角动量量子数。我们评估的对本征态的相互对齐，并发现它是独立的磁场，除了国家进行避免交叉，在这种情况下，相互作用的状态的对齐互换对应于交叉点的磁场。我们提出了一个分析模型，它提供了现成的成对对齐余弦的特点耦合转子的相互对齐的估计。
英文摘要：
We examine the rotational states of a pair of polar $^2Σ$ molecules subject to a uniform magnetic field. The electric dipole-dipole interaction between the molecules creates entangled pair-eigenstates of two types. In one type, the Zeeman interaction between the inherently paramagnetic molecules and the magnetic field destroys the entanglement of the pair-eigenstates, whereas in the other type it does not. The pair-eigenstates exhibit numerous intersections, which become avoided for pair-eigenstates comprised of individual states that meet the selection rules $ΔJ_{i}=0,\pm 1$, $ΔN_{i}=0,\pm 2$, and $ΔM_{i}=0,\pm 1$ imposed by the electric dipole-dipole operator. Here $J_{i}$, $N_{i}$ and $M_{i}$ are the total, rotational and projection angular momentum quantum numbers of molecules $i=1,2$ in the absence of the electric dipole-dipole interaction. We evaluate the mutual alignment of the pair-eigenstates and find it to be independent of the magnetic field, except for states that undergo avoided crossings, in which case the alignment of the interacting states is interchanged at the magnetic field corresponding to the crossing point. We present an analytic model which provides ready estimates of the pairwise alignment cosine that characterises the mutual alignment of the coupled rotors.
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