# Collective dynamics Using Truncated Equations (CUT-E) simulating the collective strong coupling regime with few-molecule models

Joel Yuen-Zhou University of California San Diego

Juan B. Pérez-Sánchez (a), Arghadip Koner (a), Nathaniel P. Stern (b), Joel Yuen-Zhou (a)

(a) Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, CA 92093

(b) Department of Physics, Northwestern University, Evanston, IL 60208

The study of molecular polaritons beyond simple quantum emitter ensemble models (e.g., Tavis Cummings) is challenging due to the large dimensionality of these systems (the number of molecular emitters per cavity mode is N≈106-1010), as well as the complex interplay of molecular electronic and nuclear degrees of freedom, which is absent or much reduced in atomic and solid-state polariton systems, respectively. A very important question is the extent to which single-molecule models can be used for interpretation or prediction of molecular polaritonic phenomena. In this talk, I will describe how to exploit permutational symmetries to drastically reduce the computational cost of ab-initio quantum dynamics simulations for large N [1]. In particular, we find that using an effective single molecule to calculate the dynamics in the collective regime is formally justified when N → ∞. Based on this result, which we call Collective dynamics Using Truncated Equations (CUT-E), I discuss how to seamlessly modify existing single-molecule strong coupling calculations to generate the corresponding effective models as well as the crucial differences in phenomena predicted by each type of calculation. I will also explain how to systematically derive finite N corrections to the dynamics, and show that addition of an extra surrogate molecule is enough to account for couplings that scale as O1N. As interesting applications of this formalism, I will describe how to use it to develop much needed intuition to generate robust strategies for polariton chemistry, and to apply it to describe a cavity-assisted energy funneling mechanism between different molecular species.

[1] Pérez-Sánchez, J. B., Koner, A., Stern, N. P., & Yuen-Zhou, J. (2022). Collective dynamics Using Truncated Equations (CUT-E): simulating the collective strong coupling regime with few-molecule models, arXiv preprint arXiv:2209.04955.