Campos-Gonzalez-Angulo Jorge A, Yuen-Zhou Joel
Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA.
J Chem Phys. 2022 May 21;156(19):194308. doi: 10.1063/5.0087234.
Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light-matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis-Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N × N Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.
受限电磁模式与量子发射体集合中的集体激发强烈耦合，产生被称为极化激元的光 - 物质混合态。在这种情况下，分子系统的离散多能级谱为探索多光子过程提供了一个有吸引力的平台。这项工作将塔维斯 - 卡明斯模型（其中材料是两能级系统的集合）的预测与考虑具有谐波和非谐波结构的额外能级的影响进行了对比。我们讨论了在旋转波近似下，任意数量N个振荡器集体耦合到单个腔模的精确本征谱，直至第二激发流形。详细阐述我们团队的理论方法[《新物理学杂志》23, 063081 (2021)]，我们将N×N哈密顿量的暴力对角化简化为对于任意N最多为4×4矩阵的特征分解。我们深入讨论了本征态以及弱和强非谐性的后果。此外，我们发现了双极化激元和非谐跃迁之间的共振条件，在此条件下双光子吸收可以增强。最后，我们得出结论，对于大N，由非谐性引起的极化激元态的能量 shift 变得可以忽略不计。因此，用单个或少数量子发射体进行的计算在定性上无法代表集体强耦合 regime 的非线性光学响应。我们的工作突出了耦合到腔的多能级非谐系统丰富的物理学，这在量子光学的标准模型中是不存在的。我们还提供了本征频率和跃迁振幅的简明表格表达式，这应为未来分子极化激元的光谱研究提供参考。
