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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. 

We extend our recently proposed theoretical framework for estimating cavity-modified equilibrium Fermi’s golden rule (FGR) rate constants beyond the single cavity mode case to cases where the molecular system is coupled to multiple cavity modes. We show that the cumulative effect of simultaneous coupling to multiple modes can enhance FGR rate constants by orders of magnitude relative to the single mode case. We also present an analysis of the conditions necessary for maximizing this effect in the Marcus limit of FGR-based rate theory. 

Quantum master equations (QMEs) provide a general framework for describing electronic dynamics within a complex molecular system. Off-diagonal QMEs (OD-QMEs) correspond to a family of QMEs that describe the electronic dynamics in the interaction picture based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. The fact that OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. A key experimental quantity that relies on the ability to obtain accurate Schrödinger picture electronic coherences is the absorption spectrum. In this paper, we propose using a recently introduced procedure for extracting Schrödinger picture electronic coherences from interaction picture inputs to calculate electronic absorption spectra from the electronic dynamics generated by OD-QMEs. The accuracy of the absorption spectra obtained this way is studied in the context of a biexciton benchmark model, by comparing spectra calculated based on time-local and time-nonlocal OD-QMEs to spectra calculated based on a Redfield-type QME and the non-perturbative and quantum-mechanically exact hierarchical equations of motion method.