分子與電磁極化子耦合之量子動力學：宏觀量子電動力學觀點與其在分子超輻射的應用

Abstract

分子與電磁極化子（即被介電環境修飾的光子）之間的交互作用，近年來在化學與物理領域引起廣泛關注，因其開啟了操控分子性質的全新可能性。然而，由於介電介質中光與物質耦合的複雜性，準確描述電磁極化子效應仍是一項重大理論挑戰。本論文以「宏觀量子電動力學（macroscopic quantum electrodynamics, MQED）」為基礎，系統探討複雜介電環境中量子光-物質交互作用，旨在釐清現有理論模型中的模糊之處，並揭示電磁極化子所引發的前沿物理現象。本論文聚焦於三項核心議題：(i) 從 MQED 的觀點重新檢視 TavisCummings (TC) 模型；(ii) 探討光-物質交互作用中的反旋轉項在分子與電磁極化子耦合動力學中的關鍵角色；(iii) 揭示分子聚集體與表面電漿極化子耦合下出現的異常巨大超輻射現象。本研究不僅深化我們對介電環境中光-物質交互作用的理解，也突顯電磁極化子在驅動新穎量子現象中的潛力。 在第一部分中，我們建立了 MQED 與耗散性 TC 模型之間的理論連結，並提出適用性準則：當廣義譜密度矩陣元素與分子位置無關，且呈現羅倫茲線形時，耗散 TC 模型可有效描述光-物質混合系統。此準則被進一步用於三類系統的比較分析，包含銀製 Fabry-Pérot 共振腔、銀表面與鋁製球形共振腔。結果顯示，僅有鋁製球形共振腔同時滿足上述兩項條件，顯示在使用 TC 模型時必須審慎評估其適用性。第二部分探討反旋轉項在分子量子動力學中的影響。解析結果顯示，在弱耦合極限下，若忽略反旋轉項，將導致基態分子的能量位移缺失，且近場極限下的分子間偶極-偶極作用可能出現高達 50% 的誤差。我們進一步針對一對相同分子位於電漿材料表面附近的情境，進行數值模擬與解析分析。結果顯示，在強耦合與弱耦合兩種情況下，忽略反旋轉項皆會顯著改變由偶極交互作用所引發的振盪動態，顯示在多分子系統中使用旋轉波近似時需格外謹慎。第三部分則揭示一種異常的超輻射現象，出現在分子聚集體與表面電漿極化子耦合的情況下。透過 MQED 導出的動力學方程式，我們發現電磁極化子能大幅放大超輻射效應，其規模遠超出 Dicke 預測的 N 倍放大律。為了探究此一機制，我們導出適用於任意色散與吸收性介質中之分子聚集體的超輻射速率通用解析式，並指出分子間偶極-偶極作用為觸發該異常行為的關鍵參數。本研究為理解分子聚集體中超輻射的基本機制與潛在應用提供了嶄新視角。

The interaction between molecules and polaritons (photons dressed by dielectric environments) has recently gained significant attention in both chemistry and physics as it offers new avenues for manipulating molecular properties. However, accurately modeling the effect of polaritons remains a complex theoretical challenge due to the intricate nature of light-matter interactions in dielectric media. This thesis provides a comprehensive theoretical study of quantum light-matter interactions in complex dielectric environments, employing the macroscopic quantum electrodynamics (MQED) framework for quantizing electromagnetic fields in media. Using this framework, the thesis addresses ambiguities in widely used theoretical models and investigates novel phenomena mediated by polaritons. The content is organized into three main topics: (i) revisiting the Tavis-Cummings (TC) model from the perspective of MQED, (ii) examining the essential role of counter-rotating interactions in the quantum dynamics of molecular ensembles coupled with polaritons, and (iii) exploring anomalous giant superradiance in molecular aggregates coupled to polaritons. This study deepens our understanding of light-matter interactions in complex dielectric environments and highlights the potential to uncover new phenomena driven by polaritons. In the first section, a connection between MQED and the dissipative TC model is established, formulating a guideline to assess when the TC model is applicable. This guideline specifies that the dissipative TC model can accurately represent a hybrid light-matter system if the elements of the generalized spectral density are position-independent and exhibit a Lorentzian profile. The guideline is applied to analyze the generalized spectral density's position dependence and lineshape in three systems: a silver Fabry-Pérot cavity, a silver surface, and an aluminum spherical cavity. Our findings reveal that only the aluminum spherical cavity satisfies both conditions, highlighting that the TC model's applicability requires careful consideration. In the second section, the role of counter-rotating interactions in the quantum dynamics of molecular ensembles within complex dielectric environments is investigated using MQED. The analytical analysis reveals that, in the weak coupling regime, omitting counter-rotating interactions results in the absence of medium-assisted energy shifts in ground-state molecules and significantly alters intermolecular dipole-dipole interactions-by 50% in the near-field zone. A case study on the population dynamics of a pair of identical molecules near a plasmonic surface is also conducted, showing through analytical and numerical analyses that neglecting counter-rotating interactions notably impacts the oscillatory behavior induced by dipole-dipole interactions in both strong and weak coupling regimes. These findings underscore the need for careful consideration of the rotating-wave approximation in systems with multiple molecules coupled to quantum light. Finally, in the third section, an unusual superradiance phenomenon in molecular aggregates coupled to surface plasmon polaritons is revealed. Using the dynamical equation based on MQED, it is shown that polaritons can dramatically amplify superradiance, leading to behavior that highly surpasses Dicke's N-scaling law. To elucidate the mechanism behind this phenomenon, a general analytical expression for the superradiance rate, applicable to molecular aggregates in any dispersive and absorbing medium, is derived. Additionally, the study highlights the critical role of intermolecular dipole-dipole interactions in driving this exceptional superradiance. This study paves the way for new explorations into the fundamental mechanisms of superradiance in molecular aggregates and its potential applications.