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arXiv:2604.12395

Permutationally symmetric molecular aggregates

Sricharan Raghavan-Chitra, Arghadip Koner, Joel Yuen-Zhou

quant-phphysics.opticsSubmitted Apr 14, 2026• Announced Apr 15, 2026
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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.

Comments
15 pages, 4 figures

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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→∞N \to \inftyN→∞ 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/N1/N1/N expansion that corrects the classical optics limit with finite NNN 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.
Classical optical frameworks such as the discrete dipole approximation (DDA) assume that the linear spectrum of coupled quantum emitters can be computed solely from the linear susceptibilities of individual constituents. However, recent polariton studies show that cavity linear response can encode nonlinear optical susceptibilities. Here, we demonstrate that this phenomenon is more general: emitter-emitter interactions allow nonlinearities of individual emitters to emerge in the linear response of arrays, without cavities or permutational symmetry. To illustrate this phenomenon, we show linear spectra for coupled heterodimers and linear chains, and demonstrate that Raman features of individual monomers show up as vibrational sidebands of collective resonances. Moreover, tuning Raman-type anharmonicities enables systematic control of spectral features, establishing a genuine quantum optical effect in molecular aggregates and quantum emitter arrays, which goes beyond mean-field descriptions in light-matter interactions.
The performance of approximate theories for the collective nonlinear optical response of assemblies of interacting molecules is investigated by comparing their predictions to exact calculations. To this end, the nonlinear absorption coefficient of linear molecular aggregates with energetic disorder is studied with the aid of Monte Carlo simulations. It is shown that the well-known local-field approximation (LFA) cannot describe the near-resonance nonlinear absorption spectrum for disorder values up to the nearest-neighbor intermolecular interactions; surprisingly, it is found that the validity of the LFA does not at all improve with growing disorder. By contrast, the ``excitonic two-level system'' approximation, in which each collective one-photon transition (Frenkel exciton) of the assembly is treated as an independent two-level system, turns out to describe the collective nonlinear response of the aggregates in a much better way and, moreover, rapidly improves for growing disorder values. It is shown that both models correctly describe the linear optical response and that, within the framework of the LFA, a close connection exists between the rotating-wave approximation and the Heitler-London approximation.
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We present a simple formula by which the shape of the absorption spectrum of an aggregate of quantum "monomers" (cold atoms, molecules, quantum dots, nanoparticles, etc.) interacting via dipole-dipole forces can be calculated from the averaged spectrum of the quantum monomer itself. Spectral broadening, due to a wide variety of causes, is included explicitly so that the formula is applicable not only to the idealization of a discrete spectrum but also to the practical situation of a continuously broadened spectrum. In simple cases, analytic results are obtained showing the strong dependence of the aggregate spectrum on the precise nature of the broadening of the quantum monomer spectrum. The formula is compared with results of exact diagonalization of model aggregate Hamiltonians and with experiment.
We investigate the third-order nonlinear-optical susceptibility ${\ensuremath{\chi}}^{(3)}$ in molecular aggregates and its scaling with aggregate size. The aggregate is modeled as a collection of N-interacting, homogeneously broadened two-level systems, where the interaction includes both the static dipole-dipole coupling and superradiant coupling. Our expression for ${\ensuremath{\chi}}^{(3)}$, derived using Liouville-space Green-function techniques, contains contributions from excitons as well as biexcitons. The scaling of ${\ensuremath{\chi}}^{(3)}$ with aggregate size and its dependence on the laser detuning and homogeneous and inhomogeneous dephasing rates are analyzed. ${\ensuremath{\chi}}^{(3)}$ contains terms that scale as \ensuremath{\sim}N2{N}^{2}N2 and \ensuremath{\sim}N(N-1). However, under off-resonant conditions these terms interfere destructively, resulting in a linear \ensuremath{\sim}N scaling, which is precisely what is expected for N monomers. Detailed calculations of phase-conjugate degenerate four-wave mixing and pump-probe spectroscopy are performed. In the first case we predict the existence of a narrow dephasing-induced resonance superposed on the broader superradiant exciton line shape. Pump-probe spectroscopy shows a series of biexciton absorption lines, some of which are superradiantly broadened.
Abstract The interaction between anharmonic quantum emitters (e.g. molecular vibrations) and confined electromagnetic fields gives rise to quantum states with optical and chemical properties that are different from those of their precursors. The exploration of these properties has been typically constrained to the first excitation manifold, the harmonic approximation, ensembles of two-level systems [Tavis–Cummings (TC) model], or the anharmonic single-molecule case. The present work studies, for the first time, a collective ensemble of identical multi-level anharmonic emitters and their dipolar interaction with a photonic cavity mode, which is an exactly solvable many-body problem. The permutational properties of the system allow identifying symmetry classified submanifolds in the energy spectrum. Notably, in this approach, the number of particles, typically in the order of several millions, becomes only a parameter from the operational standpoint, and the size of the dimension of the matrices to diagonalize is independent of it. The formalism capabilities are illustrated by showing the energy spectrum structure, up to the third excitation manifold, and the calculation of the photon contents as a permutationally invariant quantity. Emphasis is placed on (a) the collective (superradiant) scalings of light–matter couplings and the various submanifolds of dark (subradiant) states with no counterpart in the single-molecule case, as well as (b) the delocalized modes containing more than one excitation per molecule with no equivalent in the TC model. We expect these findings to be applicable in the study of non-linear spectroscopy and chemistry of polaritons.