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arXiv:2604.25010 · Nanophotonics

Hidden optical nonlinearities in linear spectra of quantum emitter arrays

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

physics.opticsphysics.atm-clusphysics.chem-phquant-phSubmitted Apr 27, 2026• Announced Apr 29, 2026• 1 citation
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Abstract

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.

Comments
18 pages, 10 figures

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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.
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.
Subwavelength arrays of quantum emitters offer an efficient free-space approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed photon losses and emerging optical nonlinearities due to strong photon coupling to mesoscopic numbers of emitters holds promise for generating nonclassical light and engineering effective interactions between freely propagating photons. While most studies have thus far relied on numerical simulations, we describe here a diagrammatic Green's function approach that permits analytical investigations of nonlinear processes. We illustrate the method by deriving a simple expression for the scattering matrix that describes photon-photon interactions in an extended two-dimensional array of quantum emitters and reproduces the results of numerical simulations of coherently driven arrays. The approach yields intuitive insights into the nonlinear response of the system and offers a promising framework for the systematic development of a theory for interacting photons and many-body effects on collective radiance in two-dimensional arrays of quantum emitters. Published by the American Physical Society 2024
Recent experiments have revealed ultrastrong coupling between light and matter as a promising avenue for modifying material properties, such as electrical transport, chemical reaction rates, and even superconductivity. Here, we explore (ultra)strong coupling as a means for manipulating the optical response of metamaterials based on ensembles of constituent units individually in the ultrastrong-coupling regime. We develop a framework based on linear response for quantum electrodynamical systems to study how light-matter coupling affects the optical response. We begin by applying this framework to find the optical response of a two-level emitter coupled to a single cavity mode, which could be seen as a ``meta-atom'' of a metamaterial built from repeated units of this system. We find optical behavior ranging from that of a simple two-level system (Lorentz-oscillator) to effectively transparent, as the coupling goes from the weak to deep strong-coupling regimes. We explore a one-dimensional chain of these meta-atoms, demonstrating the tunability of its optical behavior. Our scheme may ultimately provide a framework for designing metamaterials with low-loss, highly confined modes, as well as tunable (single-photon) nonlinearities.
Coupling NNN identical emitters to the same field mode is a well-established method to enhance light-matter interaction. However, the resulting N\sqrt{N}N​ boost of the coupling strength comes at the cost of a ``linearized'' (effectively semiclassical) dynamics. Here, we instead demonstrate a new approach for enhancing the coupling constant of a single quantum emitter, while retaining the nonlinear character of the light-matter interaction. We consider a single quantum emitter with NNN nearly degenerate transitions that are collectively coupled to the same field mode. We show that in such conditions an effective Jaynes-Cummings model emerges with a boosted coupling constant of order N\sqrt{N}N​. The validity and consequences of our general conclusions are analytically demonstrated for the instructive case N=2N=2N=2. We further observe that our system can closely match the spectral line shapes and photon autocorrelation functions typical of Jaynes-Cummings physics, proving that quantum optical nonlinearities are retained. Our findings match up very well with recent broadband plasmonic nanoresonator strong-coupling experiments and will, therefore, facilitate the control and detection of single-photon nonlinearities at ambient conditions.
Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of NNN anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross-section enhancements by several orders of magnitude relative to free space when the Rabi splitting ${\mathrm{\ensuremath{\Omega}}}_{R}$ is approximately equal to the molecular anharmonic shift $2\mathrm{\ensuremath{\Delta}}$. Our results provide rough upper bounds to resonant nonlinear-response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible ${S}_{0}\ensuremath{\rightarrow}{S}_{1}\ensuremath{\rightarrow}{S}_{2}$ transitions) and strongly interact with a UV-visible cavity.
An array of N closely spaced dipole coupled quantum emitters exhibits super- and subradiance with characteristic tailorable spatial radiation patterns. Optimizing the emitter geometry and distance with respect to the spatial profile of a near resonant optical cavity mode allows us to increase the ratio between light scattering into the cavity mode and free space emission by several orders of magnitude. This leads to distinct scaling of the collective coherent emitter-field coupling vs the free space decay as a function of the emitter number. In particular, for subradiant states, the effective cooperativity increases much faster than the typical linear ∝N scaling for independent emitters. This extraordinary collective enhancement is manifested both in the amplitude and the phase profile of narrow collective antiresonances appearing at the cavity output port in transmission spectroscopy.