Gera Tarun, Sebastian K L
Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India.
J Chem Phys. 2022 May 21;156(19):194304. doi: 10.1063/5.0086027.
We consider molecules confined to a microcavity of dimensions such that an excitation of the molecule is nearly resonant with a cavity mode. The molecular excitation energies are assumed to be Gaussianly distributed with mean ϵ and variance σ. We find an asymptotically exact solution for large number density N. Conditions for the existence of the polaritonic states and expressions for their energies are obtained. Polaritonic states are found to be quite stable against disorder. Our results are verified by comparison with simulations. When ϵ is equal to energy of the cavity state ϵ, the Rabi splitting is found to increase by 2σN|Ṽ|, where Ṽ is the coupling of a molecular excitation to the cavity state. An analytic expression is found for the disorder-induced width of the polaritonic peak. Results for various densities of states and the absorption spectrum are presented. The dark states turn "gray" in the presence of disorder with their contribution to the absorption increasing with σ. Lifetimes of the cavity and molecular states are found to be important, and for sufficiently large Rabi splitting, the width of the polaritonic peaks is dominated by them. We also give analytical results for the case where the molecular levels follow a uniform distribution. We conclude that the study of the width of the polaritonic peaks as a function of the Rabi splitting can give information on the distribution of molecular energy levels. Finally, the effects of (a) orientational disorder and (b) spatial variation on the cavity field are presented.
我们考虑分子被限制在一个具有特定尺寸的微腔内，使得分子的激发与腔模几乎共振。假设分子激发能呈高斯分布，均值为ϵ，方差为σ。我们找到了大量密度N时的渐近精确解。得到了极化激元态存在的条件及其能量表达式。发现极化激元态对无序相当稳定。通过与模拟结果比较验证了我们的结果。当ϵ等于腔态能量ϵ时，拉比分裂增加2σN|Ṽ|，其中Ṽ是分子激发与腔态的耦合。找到了极化激元峰的无序诱导宽度的解析表达式。给出了各种态密度和吸收光谱的结果。在存在无序的情况下，暗态变为“灰色”，其对吸收的贡献随σ增加。发现腔态和分子态的寿命很重要，对于足够大的拉比分裂，极化激元峰的宽度由它们主导。我们还给出了分子能级遵循均匀分布情况下的解析结果。我们得出结论，研究极化激元峰宽度作为拉比分裂的函数可以提供有关分子能级分布的信息。最后，给出了（a）取向无序和（b）空间变化对腔场的影响。
