Molecular polaritons are hybrid light-matter states that emerge when molecules are embedded in optical microcavities, forcing them to strongly interact with the confined electromagnetic field. In these architectures, a plethora of new molecular and optical properties have been experimentally observed during the last decade; from room temperature polariton condensation to modification of energy transfer rates, charge transfer rates, and photochemical reactivity. However, no computational methods can systematically describe the mechanisms of such modifications due to the intrinsic complexity of the system. Despite the number of molecules per light mode being enormous (from 106 to 1012, approximately), previous theoretical models of molecular polaritonic systems can afford to simulate only a handful such molecules, introducing fundamental flaws since the coupling of each individual molecule to the light is artificially increased to recover the collective coupling of the real ensemble. Consequently, some of the resulting phenomena are incompatible with realistic experimental setups. On the other hand, models that allow arbitrary number of molecules must introduce unjustified simplifications to the internal molecular degrees of freedom that are directly responsible for the phenomenology being studied. In this work we develop a powerful time-dependent formalism for molecular polaritons that acknowledges the complexity of the internal molecular structure as well as the large dimensionality of the ensemble. It capitalizes on two main ingredients: permutational symmetries arising from molecules taken to be identical, and the separation of timescales due to the interplay of collective and single-molecule coupling strengths. We demonstrate that a single effective molecule is enough to capture properties that survive in the limit of infinite molecules. Moreover, additional effective molecules can be systematically added to the system to recover properties that wane with increasing number of molecules. We call this hierarchy of few-molecule models the Collective dynamics Using Truncated Equations (CUT-E). We present the formal underpinnings of CUT-E, and use it to demonstrate a nontrivial scheme that exploits strong coupling to funnel energy from one molecular species to another.

Collective dynamics using truncated equations (CUT-E): Simulating the collective strong coupling regime with few molecule models

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