Quantum versus optical interaction contribution to giant spectral splitting in a strongly coupled plasmon–molecules system
Strong molecule-plasmon quantum interaction together with the molecule-molecule and molecule-plasmon optical interaction in a plasmon nanogap. Generally, the extrinsically visible spectral splitting observed experimentally is not equivalent to the invisible intrinsic energy level splitting of molecule.
In physics and other science disciplines, it has long been a fundamental issue to make a bridge connecting effectively and efficiently an object in the microscopic world and the observer in the macroscopic world. This is by no means an easy task and it needs great cautions, skills and wisdoms to accomplish.
The vacuum Rabi splitting, which stems from a single photon interaction with a quantum emitter (a single atom, molecule, or quantum dot), is a fundamental quantum phenomenon of long interest. Intrinsically this effect is reflected in the internal energy splitting of quantum emitter state, while extrinsically it is reflected by the spectral splitting in either photoluminescence, or fluorescence, or scattering, or absorption spectrum. Naturally there arises a fundamental and interesting question regarding whether the extrinsic spectral splitting observed by an experimenter can be exactly identical to and thus faithfully reflect the intrinsic energy level splitting of the quantum emitter state.
The quantity of vacuum Rabi splitting, ∆E∝Q/√V, where Q is the quality factor while V is the modal volume of the optical resonant cavity. This energy level splitting is usually very small, at the micro-electro volt (μeV) level. But two prominent ways can be used to increase Rabi splitting, one is to reduce the modal volume V, the other is to increase the quality factor Q.
In 2007, this splitting was increased to a few meV level by embedding a semiconductor quantum dot into a high-Q photonic crystal microcavity. Recently, many groups used plasmonic nanocavities with an extremely small modal volume V of hot spot to enhance Rabi splitting. In particular, many reports have claimed that using J-aggregates coupling to highly localized plasmon, for instance, in the nanogap formed between two closely-packed gold nanoparticles or between a sharp silver tip and a silver substrate, can produce an extremely large spectral splitting at the level of several hundred meV or even close to 1eV, the researchers called it giant Rabi splitting. Besides, this Rabi splitting is proportional to √N, where N is the number of excitons (modeled as a two-level quantum states) in J-aggregates.
More importantly, it is generally believed that this splitting originates purely from quantum interaction between excitons and plasmons, and thus should faithfully reflect the intrinsic energy level splitting of the J-aggregate quantum emitter. If this so-called giant Rabi slitting is truly the energy level splitting of microscopic particles (excitons here), it really can be called a miracle that reflects the unprecedented power of human being in manipulating, shaping and changing the microscopic world.
However, do we human beings really have so great a power? For a responsible scientist, the answer to this fundamental problem of course should be subject to a very solid scientific double-check. Prof. Zhi-Yuan Li, an expert in nanophotonics, optical physics and quantum physics from School of Physics and Optoelectronic Technology, South China University of Technology, together with his PhD student Bo Wang and Xian-Zhe Zeng, a visiting undergraduate student from School of Physics, Peking University, took this issue into careful and deliberate examination, trying to figure out the truth. They have carried out a deep theoretical research of plasmon-molecule interaction and set up a theoretical model which can handle complicated quantum and optical interactions and distinguish their individual contribution to the observed spectral splitting that are hard to elucidate via pure experimental studies. Related research results are published in Photonics Research, Vol. 8, Issue 3, 2020 (Bo Wang, Xian-Zhe Zeng, Zhi-Yuan Li. Quantum versus optical interaction contribution to giant spectral splitting in a strongly coupled plasmon–molecules system[J]. Photonics Research, 2020, 8(3): 03000343).
The team first noticed that in these experiments claiming giant Rabi splitting, the observed quantity, strictly speaking, is rather a giant spectral splitting. So, a problem naturally arises whether this extrinsic spectral splitting is equivalent to the intrinsic energy level splitting (the original meaning of Rabi splitting).
To explicitly answer this question, the team also noticed that the plasmon-molecule interaction takes place not only in the quantum mechanical level in terms of single-molecule Rabi splitting but also in the classical optical level in terms of multiple scattering between molecules and plasmons. When the plasmon nanogap involves more molecules, as is the case in most experiments, there also exists multiple scattering among these molecules and their multiple scattering interaction with the nanogap plasmon. In short, the observed extrinsic spectral splitting in principle should stem both from the quantum interaction of single-molecule with plasmons (Rabi splitting) and from the classical optical interaction of multiple molecules with plasmons.
More precisely, the quantum interaction of highly localized plasmon hot spot field upon each individual molecule will cause an energy level splitting, the true Rabi splitting, with the quantity depending on the molecule exciton dipole moment and the field amplitude. This quantum interaction will change a lot the response of the molecule (compared with usual weak-field situation) against the incident light, including the dipole moment strength and its spectral lineshape. This molecule, with a greatly modified optical response, will in turn affect the interaction of external light with the nanogap plasmons. Obviously, this is a classical optical interaction. When N molecules are involved, they will together significantly modify the optical property (more specifically the effective refractive index) of the background medium sensed by this nanogap plasmon and thus greatly change the scattering spectrum of the molecule-plasmon system against the incident light signal, leading to the observed spectra of optical signal with a feature of giant splitting.
This expectation has been confirmed by the team's numerical simulations, which show that the scattering spectrum is very sensitive to the surrounding medium filling the plasmonic nanogap, where an apparent spectral shift is clearly visible upon changing the refractive index of the medium. This high sensitivity is of course well known in the community of nanophotonics, and also well recognized as a purely optical effect originating from the complicate optical interaction between the highly localized nanogap plasmon hot spot with the medium surrounding it.
To be more quantitative, the team developed a Lorentzian model to approximately describe molecules and plasmon, describe the optical response of all the molecules, and calculate the effective refractive index of the molecule system as a filling medium against the nanogap plasmon. Then they found that the collective optical interaction is dominant to generate the giant splitting (in scattering spectra), which is also proportional to √N, over the quantum interaction of single-molecule Rabi splitting.
Therefore, the observed giant spectral splitting is not a pure quantum Rabi splitting effect, but rather a mixture contribution from the large spectral modulation by the collective optical interaction of all molecules with plasmons and the modest quantum Rabi splitting of single-molecule strongly coupled with plasmons. The physical insights and theoretical model developed by this team can offer a more reasonable angle to look into the complicated molecule-plasmon strong interacting system. This theory can help to figure out the true quantity of the intrinsic energy level splitting of microscopic molecule, answer the question of how large the true Rabi splitting can be, and more importantly, find out the true power of human being and the limitation to change the microscopic world.
This work also suggests that nature behaves more complicated than it hints at a first glance, and therefore, one should develop a broad vision when looking into light-matter interaction at nanoscale in order to get deep physical insight and find the most important key to a seemingly simple optical phenomenon.
Prof. Huakang Yu, an optics expert from the same optics group led by Zhi-Yuan Li, says: "Investigating interactions between surface plasmon polaritons and metallic nanostructures is very popular recently. The strong localized electric fields of nanogap plasmons could lead to significant spectral changes, i.e., Rabi splitting, which is from the full quantum mechanical description with various parametric inputs. This research successfully explained the observed spectral splitting from the classical optical interaction of multiple molecules with plasmons, thus questioned the validity of the pure quantum mechanial descriptions presented previously. Indeed, the research results reflects the fact that experimental imperfections such as surface-ligand interactions or inhomogeneity could possibly contribute to the measured plasmonic resonance spectrum, making the experiments of quantum plasmonics not easy to handle.”
The next thing the team will do is to extend the model from a multiple-molecule system to a single molecule involving multiple microscopic excitons, clarify the true energy splitting of each exciton, and find out the contribution of quantum and optical interaction in this single molecule level (but still not the single exciton level). Besides, it is also interesting to construct a more accurate model that can describe well the quantum and optical interaction in the strong interacting molecule-plasmon system and disclose possible mutual competing and cooperating action of these two effects.
分子-等离激元强耦合系统之光谱劈裂：量子起源还是光学起源？
金属纳米间隙分子-等离激元量子和光学相互作用的物理原理图。该图描述了分子-等离激元间的强量子相互作用以及分子-分子和分子-等离激元的光学相互作用。由于量子和光学相互作用的共同参与，通常实验观测到的频谱劈裂并不等价于分子内量子态的能级劈裂。
构建一座顺畅通达的桥梁以连接微观世界的物质和宏观世界的观察者，是物理学和许多自然科学分支的一个重要而艰巨的任务。而经历了150年发展的光谱学技术已经成为了完成此项任务的强大工具。
真空拉比劈裂（Rabi splitting）来源于单光子和单个量子辐射体（单个原子、分子或者量子点）间的强相互作用，是微观世界的基本量子现象之一。从内在本质上说，这个现象反映了量子辐射体内量子态的能级劈裂；而从外在表征上说，该现象可通过光致发光谱、荧光光谱、散射谱和吸收谱中呈现的光谱劈裂反映出来。很自然地，就产生了一个有趣的基础性科学问题：实验者观察到的光谱劈裂是否可以与量子辐射体内的本征能级劈裂画上等号，从而真实地反映量子辐射体的能态演化及劈裂现象？
真空拉比劈裂量∆E通常来说比较小,在μeV量级。多年的研究表明，可以利用光学谐振腔增强拉比劈裂。近年来的研究表明，利用极小模体积的等离激元纳米腔（plasmon nanocavity）可以增强拉比劈裂：将J-分子聚合体置于等离激元纳米间隙（nanogap）中，可与高度局域化的等离激元发生强耦合，进而产生几百甚至上千meV的巨拉比劈裂（giant Rabi splitting）。研究人员普遍认为这种劈裂纯粹地源于激子和表面等离激元之间的量子相互作用，并且如实地反映了J-分子聚合体量子辐射体的本征能级劈裂。如果这个所谓的巨拉比劈裂真的是微观粒子（这里是激子）的能级劈裂，那实在可以说是一个奇迹，因为它反映了人类在操纵、塑造和改变微观世界方面拥有了前所未有的力量。
但是，我们人类真的有这么大的力量吗？对于一个负责任的科学家来说，获得这个基本问题的答案一定要经过非常扎实、严格而审慎的研究及审核过程。
华南理工大学物理与光电学院的纳米光子学、光学物理和量子物理专家李志远教授带领博士生王博和北京大学物理学院访学本科生曾宪哲，对金属纳米间隙中分子-等离激元强耦合体系中存在的量子和光学相互作用，以及两者对内在的能级劈裂以及外在的光谱劈裂所起的贡献等基础物理问题进行了详细而深入的理论研究，建立了一个能够处理复杂的量子和光学相互作用的理论模型，并能区分它们对实验观测到的光谱劈裂的贡献。相关研究成果作为封面文章发表在Photonics Research 2020年第8卷第3期上（Bo Wang, Xian-Zhe Zeng, Zhi-Yuan Li. Quantum versus optical interaction contribution to giant spectral splitting in a strongly coupled plasmon–molecules system[J]. Photonics Research, 2020, 8(3): 03000343）。
该研究小组首先注意到，在这些声称得到巨拉比劈裂的实验中，严格地说，观测到的实际上是巨大的光谱劈裂。因此，自然会产生这样一个问题：这些外在的光谱劈裂是否等同于内在的能级劈裂（拉比劈裂的原始含义）。为了明确地回答这个问题，研究小组还注意到，等离激元与分子间的相互作用不仅发生在单分子拉比劈裂的量子力学水平上，而且也发生在分子与等离激元之间多层散射的经典光学水平上（如下图所示）。当等离激元纳米间隙包含更多的分子时，如大多数实验中的情况一样，还存在分子之间的多重散射及其与等离激元间的多重散射相互作用。
简而言之，实验所观察到的光谱劈裂，原则上既来源于单分子与等离激元的量子相互作用（拉比劈裂），也来源于单分子/多分子与等离激元间的经典光学相互作用。更准确地说，高度局域的等离激元热点光场与单个分子的量子相互作用将导致能级劈裂，即真正的拉比劈裂，其劈裂量取决于分子内激子偶极矩和单光子场强的大小。这种量子相互作用会改变分子对入射光的响应，包括偶极矩强度和谱线形状。反过来，分子的光学响应会进一步影响外光场与等离激元纳米间隙的相互作用，显然这是一种经典的光学相互作用。当涉及N个分子时，它们将显著地改变纳米间隙等离激元其背景介质的光学性质（有效折射率和介电常数），从而极大地改变分子-等离激元系统的散射光谱，导致观测到的光信号呈现巨大的光谱劈裂特征。
研究小组的数值模拟证实了这一预期。结果表明，散射光谱对在等离激元纳米间隙内填充的介质其折射率改变是非常敏感的。当介质折射率改变时，将发生明显的光谱位移。
为了使分析更加定量，研究小组利用洛伦兹模型来近似地描述分子和等离激元。该模型描述了所有分子的光学响应，并计算了作为填充介质的分子对纳米间隙等离激元的有效折射率。研究发现，相比于单分子拉比劈裂的量子相互作用，分子集体与纳米间隙等离激元的光学相互作用，是产生巨大光谱劈裂的主要原因。因此，许多实验所观察到的巨大光谱劈裂不是纯粹的量子拉比劈裂效应，而是所有分子与等离激元集体光学相互作用所引起的巨大频谱调制效应和单分子与等离激元强耦合的量子拉比劈裂所引起的较小光谱调制效应的协同作用之总和。
这项研究提出的物理观点和理论模型为研究复杂的分子-等离激元间的强相互作用系统提供了一个更合理的物理学角度。该理论有助于理清微观分子在单光子光场驱动下的内在能级劈裂的真实大小，了解真实的量子拉比劈裂能达到的数量级。更重要的是，回答人类能够在多大程度上改变微观世界这一根本的科学问题。这项工作还表明，自然界的行为往往比表面看起来要复杂得多、"狡猾”得多。因此，在研究纳米、亚纳米、乃至原子尺度上的光和物质相互作用时，应该开拓广阔的视野，打破单学科的局限性，以便获得对复杂自然事物和实验现象之深刻而完整的物理理解，并找到看似简单的光学现象背后所实际隐藏的关键物理机制，从而推动物理学向未知领域的前进步伐。