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arXiv:2604.03423

Universal Scaling and Many-Body Resurrection of Polaritonic Double-Quantum Coherences

Maxim Sukharev

physics.chem-phcond-mat.mes-hallquant-phSubmitted Apr 3, 2026• Announced Apr 7, 2026• 0 citations• Revised Apr 10, 2026 (v2)
v1 · Apr 3, 2026v2 · Apr 10, 2026v3 · May 8, 2026
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Abstract

The ultrafast nonlinear optical response of molecular ensembles is fundamentally altered under strong light-matter coupling. To rigorously isolate the genuine many-body contributions, an exact time-domain field-subtraction protocol is developed within a fully non-perturbative Maxwell-Liouville framework explicitly incorporating the two-exciton manifold in real space and time. This approach reveals that while collective cavity delocalization drives the macroscopic nonlinear signal toward a severe harmonic cancellation (an effect termed "spectral starvation"), intrinsic many-body molecular interactions robustly resurrect genuine polaritonic double-quantum coherences (DQCs). This many-body resurrection is governed by a universal two-photon matching rule, $Δ_B + 4J = Ω_R$, linking molecular anharmonicity ($Δ_B$) to the macroscopic Rabi splitting ($Ω_R$) and excitonic coupling ($J$). Crucially, this resonance exploits the spatial mismatch between macroscopic polaritons and localized two-exciton pairs to break harmonic cancellation. For J-aggregates ($J < 0$), this condition uniquely isolates the resonant many-body state below the dense manifold of localized dark states, protecting the macroscopic coherence from spatial fragmentation. This predictive framework establishes a direct phase diagram to engineer and protect optical nonlinearities across diverse strongly coupled platforms.

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The ultrafast nonlinear optical response of molecular ensembles is fundamentally altered under strong light-matter coupling. To rigorously isolate the genuine many-body contributions, an exact time-domain field-subtraction protocol is developed within a fully non-perturbative Maxwell-Liouville framework explicitly incorporating the two-exciton manifold in real space and time. This approach reveals that while collective cavity delocalization drives the macroscopic nonlinear signal toward a severe harmonic cancellation (an effect termed "spectral starvation"), intrinsic many-body molecular interactions robustly resurrect genuine polaritonic double-quantum coherences (DQCs). This many-body resurrection is governed by a universal two-photon matching rule, ΔB+4J=ΩRΔ_B + 4J = Ω_RΔB​+4J=ΩR​, linking molecular anharmonicity (ΔBΔ_BΔB​) to the macroscopic Rabi splitting (ΩRΩ_RΩR​) and excitonic coupling (JJJ). Crucially, this resonance exploits the spatial mismatch between macroscopic polaritons and localized two-exciton pairs to break harmonic cancellation. For J-aggregates (J<0J < 0J<0), this condition uniquely isolates the resonant many-body state below the dense manifold of localized dark states, protecting the macroscopic coherence from spatial fragmentation. This predictive framework establishes a direct phase diagram to engineer and protect optical nonlinearities across diverse strongly coupled platforms.
We present a general and efficient approach to compute phase-resolved multidimensional spectra of anharmonic molecular polaritons, based on a semiclassical evolution of the molecular Hamiltonian and cavity field in the large-N\mathcal{N}N limit of many molecules coupled to a confined photonic mode. By systematically expanding the response in both amplitudes and phases of the input fields, our method enables a transparent and computationally simple construction of phase-cycled two-dimensional single- and double-quantum polariton spectra from the underlying nonlinear signal components. Here, phase cycling acts as an analogue of phase matching with oblique pulses, allowing for the isolation of the contributing nonlinear pathways in Liouville space. We specialize to vibrational polaritons and benchmark the method through direct comparison with experimentally measured single-quantum spectra, providing an explanation for the longstanding puzzle of the polariton bleach effect observed at short waiting times. Further, we show how the imprint of various types of anharmonicities on the double-excitation manifold can be directly probed and analyzed through double-quantum coherence spectroscopy. Taken together, our results establish a practical and powerful framework for the modeling and interpretation of nonlinear spectroscopic experiments on strongly coupled light-matter platforms and for guiding the design of cavity-enhanced molecular platforms.
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.
We study a hybrid system of coupled cavities, with or without two-level atoms doped inside. By employing a building-block construction facilitated by nonlinear Stark coupling, we identify a manifold of exact many-body eigenstates that remain analytically tractable across arbitrary lattice geometries and atom distributions. We demonstrate that these exact states exhibit a dual physical nature depending on their spectral positioning: when embedded within the chaotic many-body spectrum, they manifest as quantum scars that violate the eigenstate thermalization hypothesis and undergo weak ergodicity breaking; conversely, as ground states within fixed-total-excitation sectors, they exhibit off-diagonal long-range order and form polariton condensates. Furthermore, numerical calculations of local excitation-number fluctuations suggest that negative Stark coupling shifts the Mott-insulator to superfluid transition toward weaker inter-cavity hopping. Our findings provide a versatile framework for engineering both coherent quantum phases and non-thermalizing states in diverse light-matter architectures.
Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light–matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis–Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N2 × N2 Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.
The field of Polaritonic Chemistry studies molecules strongly coupled to the light field of optical cavities. The resulting modification of the potential energy landscape has been demonstrated to enable control over the chemical and physical properties of materials and molecular ensembles. This thesis extends the Tavis–Cummings model to describe molecules under strong light–matter coupling, incorporating static dipole moments and dipole self-energy contributions derived from the Pauli–Fierz Hamiltonian. These additional terms are shown to be essential for reproducing cavity-modified molecular dynamics and spectra. Simulations on the nuclear wavefunction propagation of MgH+ molecules demonstrate the impact of these terms, while an effective two-level system model accurately captures the behavior of large ensembles. Beyond single excitations, the thesis also explores the higher excitation manifolds of the Tavis-Cummings model, which reveals that allowing for more than a single excitation makes the reaction of the involved polaritons entropically more favorable. Open-system simulations highlight how the coherence of the system's initial state governs decay pathways and enables long-lived energy storage. Finally, a multilevel vibrational model coupled to a two-mode cavity is introduced, where a Raman scheme enables selective mixing of vibrational states. The simulation results show that continuous pumping can drive molecules into specific vibrational states while suppressing electronic excitation, both for single molecules and small ensembles. Together, these results provide new theoretical insights into the mechanisms by which optical cavities reshape molecular energy landscapes. The results suggest approaches for controlling photonic, electronic, and vibrational dynamics in strongly coupled systems, contributing to the theoretical foundation of polariton chemistry.
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.