Supersymmetry, entanglement, and dynamics of polar paramagnetic molecules subject to combined electric, magnetic, and optical fields

与外界电场、磁场或光场的相互作用提供了操纵中性气相分子旋转和平移运动的主要手段。在最近的发展中，有控制分子取向和/或排列的新方法，以及偏转和聚焦其平移运动和实现分子捕获的方法。取向的重要性也体现在光的新应用中，如获得时间分辨的光电子角分布、内部衍射、光解离产物的分离、去电子、高次谐波产生和轨道成像、量子模拟和量子计算。在这里，我们建议研究电场、磁场和光场的组合作用下的极性顺磁分子。极性顺磁分子中最突出的例子是普遍存在的二重态Sigma、三重态Sigma和二重态PI线性物种，如SRF、SO和OH。含有稀土原子的异核双原子或更大的极性分子通常表现出更高的轨道和自旋电子角动量，因此，相应地也有更大的磁偶极矩。极性顺磁分子的相反宇称塞曼能级在磁场的特定值相交，在该磁场下，它们可以被叠加的弱电场有效地耦合。我们的初步结果表明，叠加光场可以产生附加能级的近简并，这些附加能级可以通过静电场(或分子系综中的电偶极-偶极相互作用)耦合。因此，三场组合可以实现例如偶极取向的快速切换和仅在双磁场和电场组合中不能获得的其他动态效果。我们计划在电场、磁场和光场的三重组合中研究极性顺磁分子的超对称性和纠缠。就像在静电场和光场中的极性分子和可极化分子的情况一样，我们希望它们的超对称性将引导我们得到它们的本征性质的解析形式。此外，我们将绘制出各种分子几何阵列的可实现的纠缠，从而为量子计算的替代平台铺平道路。我们还建议研究极性顺磁分子的动力学，以适应光场的时间依赖关系，并将控制策略与组合场中基本分子能量超曲面的拓扑联系起来，特别强调它们的Stark和Zeeman能面的圆锥形交点的突出作用。我们预计，这可能导致新的方法来设计有效的和特定于状态的激励方案的控制场。这些将包括对量子门的控制，这是利用分子进行量子计算的关键组成部分。

Interactions with external electric, magnetic or optical fields provide the chief means to manipulate the rotational and translational motion of neutral gas-phase molecules. Among recent developments are new methods to control the orientation and/or alignment of molecules as well as methods to deflect and focus their translational motion and to achieve molecular trapping. The importance of orientation comes also to light in novel applications such as attaining time-resolved photoelectron angular distributions, diffraction-from-within, separation of photodissociation products, deracemization, high-order harmonic generation and orbital imaging, quantum simulation and quantum computing.Herein we propose to study polar paramagnetic molecules subject to a combination of electric, magnetic, and optical fields. Among the most prominent examples of polar paramagnetic molecules are the ubiquitous doublet Sigma, triplet Sigma, and doublet Pi linear species, such as SrF, SO, and OH. Heteronuclear diatomics or larger polar molecules that contain a rare-earth atom often exhibit much higher orbital and spin electronic angular momenta and, therefore, correspondingly larger magnetic dipole moments. The opposite-parity Zeeman levels of polar paramagnetic molecules intersect at a particular value of the magnetic field at which they can be efficiently coupled by a superimposed weak electric field. Our preliminary results suggest that a superimposed optical field may create near-degeneracies of additional levels that could be coupled by the electrostatic field (or the electric dipole-dipole interaction in a molecular ensemble). Thereby, the triple-field combination could enable for instance fast switching of dipolar orientation and other dynamical effects that are not available in a dual magnetic and electric field combination alone. We plan to study the supersymmetry and entanglement of polar paramagnetic molecules in the triple-combination of electric, magnetic and optical fields. Like in the case of polar and polarizable molecules in combined electrostatic and optical fields, we hope that their supersymmetry will guide us to an analytic form of their eigenproperties. Furthermore, we will map out the achievable entanglement for a variety of geometric arrays of molecules and thereby pave the way for an alternative platform for quantum computing. We also propose to investigate the dynamics of polar paramagnetic molecules for a tailored time-dependence of the optical field and to connect the control strategies to the topology of the underlying molecular energy hypersurface in the combined fields, with special emphasis on the prominent role of the conical intersections of their Stark and Zeeman energy surfaces. We expect that this may lead to novel approaches to designing control fields for efficient and state-specific excitation schemes. These will include the control of quantum gates, a key ingredient of quantum computing with molecules.