Lai Yifan, Ying Wenxiang, Huo Pengfei
Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA.
The Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, USA.
J Chem Phys. 2024 Sep 14;161(10). doi: 10.1063/5.0231396.
We derive an analytic expression of the non-equilibrium Fermi's golden rule (NE-FGR) expression for a Holstein-Tavis-Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi's golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.
我们推导了用于荷斯坦 - 塔维斯 - 卡明哈密顿量的非平衡费米黄金规则（NE - FGR）表达式，这是一个用于许多分子集体耦合到光学腔的通用模型。这些NE - FGR表达式捕捉了从极化激元态到暗态跃迁速率常数的全时变行为。结果表明，在平衡和集体极限下，该速率可简化为著名的基于频域的平衡费米黄金规则（E - FGR）表达式，并且在非平衡和非集体情况下，其与位点数量的缩放关系保持不变。我们使用这些NE - FGR通过时间非局部和时间局部量子主方程来进行布居动力学研究，并从初始占据的上极化激元态或下极化激元态获得准确的布居动力学。此外，与E - FGR理论相比，从下极化激元态开始时，NE - FGR显著提高了布居动力学的准确性，突出了非马尔可夫行为和跃迁速率常数中短时间瞬态行为的重要性。
