電子-核-光子系統的非絕熱量子電動力學效應

Abstract

量子電動力學非絕熱輻射(quantum electrodynamic non-adiabatic emission, QED-NAE)是一種新穎的輻射機制，驅動此過程的是電子、原子核與光子之間的非絕熱交互作用。本論文發展了一套完整的理論框架，用以分析 QED-NAE ，並將此機制的理論從單一共振腔光子模式(single cavity photonic mode, SCM)情形擴展至包含無限多光子模式(infinite photonic modes, IPM)的情形，後者貼切地描述了真空狀態。我們利用一般性波恩-黃展開(generalized Born-Huang expansion)，推導出包含所有分子與光子交互作用的非絕熱耦合(non-adiabatic coupling)，並結合費米黃金定則(Fermi's golden rule)，即可定量計算 QED-NAE 之速率常數。

透過第一原理計算，我們分析了9-氰基蒽在 SCM 與 IPM 兩種情境下的 QED-NAE 速率常數。計算結果揭示了影響 QED-NAE 過程的三個主要因素：決定光物質耦合強度的模態體積(mode volume)；反映分子振動、電子躍遷與光子偏振間相對取向的質量加權取向因子 (mass-weighted orientation factor)；以及描述電磁模式的光子態密度(photonic density of states)。

結果指出，即使 IPM 情境提供了無限多的光子模式， QED-NAE 速率的整體提升仍十分有限。這種限制主要來自真空中光與物質本質上的微弱耦合，故只有在特定條件下， QED 效應才可能顯著改變非絕熱過程。因此，本論文不僅提供了一個理解非絕熱 QED 效應的統一理論基礎，亦為未來實驗與理論上進一步探索光子對化學過程的影響提供了可能的途徑。

Quantum electrodynamic non-adiabatic emission (QED-NAE) is a novel radiative mechanism driven by non-adiabatic interactions among electrons, nuclei, and photons. In this thesis, we develop a comprehensive theoretical framework to analyze QED-NAE, extending the analysis from a single cavity photonic mode (SCM) scenario to infinite photonic modes (IPM) scenario, which realistically represents free-space conditions. Utilizing generalized Born-Huang expansion approach, we derive explicit expressions for non-adiabatic couplings (NACs) that incorporate all photon-molecule interactions. These NACs, when applied within Fermi's golden rule, enable quantitative calculations of the QED-NAE rate constants.

Employing first-principles computations, we specifically investigated the QED-NAE rate constants of 9-cyanoanthracene under both SCM and IPM scenarios. Our results identify three primary factors influencing the QED-NAE process: the mode volume, which determines the strength of light-matter coupling; the mass-weighted orientation factor, reflecting alignment between molecular vibrations, electronic transitions, and photonic polarization; and the photonic density of states, characterizing the availability of resonant electromagnetic modes.

The comparative analysis demonstrates that although the IPM scenario provides an infinite number of photonic modes, the overall enhancement in the QED-NAE rate remains limited. This limitation arises primarily due to inherently weak light-matter coupling strengths in free space, underscoring that significant QED-induced modifications to non-adiabatic processes are only feasible under specific conditions. Thus, this thesis not only offers a unified theoretical foundation for understanding non-adiabatic QED effects but also provides a possible avenue for future experimental and theoretical explorations of photonic influences on chemical processes.