Vibrational Dressing of Collective Molecular Polaritons: A Scalable Green's-Function Theory
Abstract
We develop a scalable Green's-function theory of vibrationally dressed molecular-polariton absorption in the Holstein--Tavis--Cummings model. Within the self-consistent Born approximation (SCBA), the ground-state linear response of N identical molecules coupled to one cavity mode follows from a 2×2 cavity--bright matrix, while scattering through the N−1 dark states remains in the molecular self-energy. The number of self-consistent equations is independent of N, allowing large ensembles to be treated without explicitly resolving the dark manifold. Benchmarks against hierarchical equations of motion show that the theory captures collective linewidth narrowing and an N-dependent minimum in the lower-polariton linewidth as its exciton fraction varies, beyond a Hopfield-weighted linewidth estimate. Comparisons with exact diagonalization for discrete local vibrations show weaker vibronic progressions and better overall SCBA agreement as N increases at fixed single-molecule coupling. The resulting framework connects microscopic vibrational scattering to collective absorption spectra without introducing fitted polariton linewidths.
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BibTeX
@misc{ying2026vibrational,
title = {{Vibrational Dressing of Collective Molecular Polaritons: A Scalable Green's-Function Theory}},
author = {Wenxiang Ying and Michael Galperin and Abraham Nitzan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20912},
eprint = {2610.20912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20912},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Vibrational Dressing of Collective Molecular Polaritons: A Scalable Green's-Function Theory
AU - Wenxiang Ying
AU - Michael Galperin
AU - Abraham Nitzan
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20912
UR - https://arxiv.org/abs/2610.20912
AB - We develop a scalable Green's-function theory of vibrationally dressed molecular-polariton absorption in the Holstein--Tavis--Cummings model. Within the self-consistent Born approximation (SCBA), the ground-state linear response of N identical molecules coupled to one cavity mode follows from a 2×2 cavity--bright matrix, while scattering through the N−1 dark states remains in the molecular self-energy. The number of self-consistent equations is independent of N, allowing large ensembles to be treated without explicitly resolving the dark manifold. Benchmarks against hierarchical equations of motion show that the theory captures collective linewidth narrowing and an N-dependent minimum in the lower-polariton linewidth as its exciton fraction varies, beyond a Hopfield-weighted linewidth estimate. Comparisons with exact diagonalization for discrete local vibrations show weaker vibronic progressions and better overall SCBA agreement as N increases at fixed single-molecule coupling. The resulting framework connects microscopic vibrational scattering to collective absorption spectra without introducing fitted polariton linewidths.
ER -