Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States.
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, United States.
J Am Chem Soc. 2020 Jun 10;142(23):10446-10458. doi: 10.1021/jacs.0c02808. Epub 2020 Jun 2.
The use of a nonclassical light source for studying molecular electronic structure has been of great interest in many applications. Here we report a theoretical study of entangled two-photon absorption (ETPA) in organic chromophores, and we provide new insight into the quantitative relation between ETPA and the corresponding unentangled TPA based on the significantly different line widths associated with entangled and unentangled processes. A sum-over-states approach is used to obtain classical TPA and ETPA cross sections and to explore the contribution of each electronic state to the ETPA process. The transition moments and energies needed for this calculation were obtained from a second linear-response (SLR) TDDFT method [, , , 204105], which enables the treatment of relatively large polythiophene dendrimers that serve as two-photon absorbers. In addition, the SLR calculations provide estimates of the excited state radiative line width, which we relate to the entangled two-photon density of states using a quantum electrodynamic analysis. This analysis shows that for the dendrimers being studied, the line width for ETPA is orders of magnitude narrower than for TPA, corresponding to highly entangled photons with a large Schmidt number. The calculated cross sections are in good agreement with the experimentally reported values. We also carried out a state-resolved analysis to unveil pathways for the ETPA process, and these demonstrate significant interference behavior. We emphasize that the use of entangled photons in TPA process plays a critical role in probing the detailed electronic structure of a molecule by probing light-matter interference nature in the quantum limit.
非经典光源在研究分子电子结构方面的应用在许多应用中引起了极大的兴趣。在这里，我们报告了对有机发色团中纠缠双光子吸收（ETPA）的理论研究，并根据纠缠和非纠缠过程相关的显著不同的线宽，提供了对 ETPA 与相应的非纠缠 TPA 之间定量关系的新见解。采用态和方法来获得经典 TPA 和 ETPA 截面，并探索每个电子态对 ETPA 过程的贡献。此计算所需的跃迁矩和能量是从二次线性响应（SLR）TDDFT 方法[3,4,5,204105]中获得的，该方法能够处理用作双光子吸收体的相对较大的聚噻吩树状大分子。此外，SLR 计算提供了激发态辐射线宽的估计值，我们使用量子电动力学分析将其与纠缠双光子态密度相关联。该分析表明，对于正在研究的树状大分子，ETPA 的线宽比 TPA 的线宽窄几个数量级，对应于具有大 Schmidt 数的高度纠缠光子。计算出的截面与实验报道的值吻合良好。我们还进行了状态分辨分析，以揭示 ETPA 过程的途径，这些途径表现出明显的干涉行为。我们强调，在 TPA 过程中使用纠缠光子在量子极限下探测光物质干涉性质对于探测分子的详细电子结构起着至关重要的作用。
