Permutationally symmetric molecular aggregates

TL;DR

This paper identifies a limit where classical optics methods are exact for permutationally symmetric molecular aggregates of infinite size, and explores finite-size corrections revealing quantum optical features.

Contribution

It establishes a quantum mechanical limit for classical optics methods in symmetric aggregates and introduces a $1/N$ expansion for finite-size corrections.

Findings

Classical optics methods are exact for infinite permutationally symmetric aggregates.

Finite-size corrections include Raman-like transitions of a single monomer.

The results clarify how quantum optical features can appear in simple molecular arrays.

Abstract

Linear optical spectra of molecular aggregates are often approximated by classical optics methods such as the discrete-dipole approximation (DDA), coherent exciton scattering (CES), and coherent potential approximation (CPA), where the only quantum-mechanical input to the calculation is the linear susceptibility of the monomers. However, the limits of validity of these classical optics methods remain opaque. Here, starting from a quantum mechanical Hamiltonian for the aggregate, we identify a limit where DDA/CPA/CES is exact: all-to-all coupled permutationally symmetric aggregates of $N \to \infty$ monomers. The permutational symmetry of this molecular version of the Lipkin-Meshkov-Glick model, which is closely related to that of the molecular polariton problem of many identical molecules coupled to a single-cavity mode, allows us to borrow recent techniques developed for the latter. In particular, we identify a $1/N$ expansion that corrects the classical optics limit with finite $N$ corrections to the linear response of the aggregate. These corrections feature as Raman-like transitions of a single monomer. We illustrate these findings with calculations on the very physically-relevant setup of a homodimer. Our findings clarify how quantum optical features that go beyond classical optics can already be present in simple arrays of quantum emitters such as molecular aggregates.