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

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 dictates that J-aggregates ($J < 0$) uniquely isolate the resonant many-body state below the dense two-exciton scattering continuum, 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.

Figures (4)

• Figure 1: (a) Schematic of the pump-probe heterodyne detection setup for a molecular ensemble strongly coupled to an optical cavity. (b) Linear optical response establishing the strong coupling regime. The black line shows transmission for the empty cavity. Red and blue lines display the out-of-cavity molecular absorption for low ($3\times10^{19}$ cm$^{-3}$, red) and high ($10^{20}$ cm$^{-3}$, blue) molecular densities. The corresponding in-cavity transmission profiles (green and purple lines) illustrate the macroscopic Rabi splitting and the formation of the lower and upper polariton ($\omega_\mathrm{LP}$ and $\omega_\mathrm{UP}$) branches. Mirror-to-mirror distance is 305.5 nm.
• Figure 2: Breakdown of the harmonic approximation and the onset of spectral starvation. 2D heterodyne signal amplitude for the high-density ($10^{20}$ cm$^{-3}$) system evaluated at zero molecular anharmonicity ($\Delta_B=0$). (a) Out-of-cavity (slab) response exhibiting a single peak at the bare molecular resonances. (b) In-cavity response showing polaritonic splitting. The white dashed grid indicates the fundamental ($\omega_\mathrm{LP}$, $\omega_\mathrm{UP}$) and harmonic sum frequencies ($2\omega_\mathrm{LP}$, $2\omega_\mathrm{UP}$, $\omega_\mathrm{LP}+\omega_\mathrm{UP}$). Despite identical molecular densities, the maximum field amplitude in the cavity is starved relative to the bare slab, reflecting the suppression of population-modulation artifacts by the collective delocalization of the single-exciton manifold.
• Figure 3: Spectral migration and many-body resurrection of the genuine double-quantum coherence (DQC). The in-cavity low-density response ($3\times10^{19}$ cm$^{-3}$) is shown for increasing molecular anharmonicities: (a) $\Delta_B = 50$ meV, (b) $\Delta_B = 120$ meV, and (c) $\Delta_B = 180$ meV. The genuine DQC peak systematically detaches from the harmonic sum frequencies of the single-exciton manifold (indicated by the dashed grid). Maximum resurrection is observed in panel (b), where the molecular anharmonicity, $\Delta_B$, matches the Rabi frequency, $\Omega_R$, maximizing the coupling between the polariton states and the localized many-body manifold. The white dashed lines crossing in the center of each panel denote the uncoupled bare molecule resonances ($\omega_e$ and $2\omega_e$) for reference.
• Figure 4: Scaling of the nonlinear signal amplitude, time-resolved spatial delocalization, and the universal phase diagram. For each $J$-case, the bare cavity is tuned to the maximum molecular absorption of the respective aggregate. (a) In-cavity peak DQC amplitudes for the low-density system comparing the uncoupled molecular control (black; $J=0$ meV) with H-aggregate (red; $J=30$ meV) and $J$-aggregate (blue; $J=-30$ meV) configurations. All curves are normalized to the peak signal of the $J=0$ control. The many-body interactions within the molecular manifold fundamentally rewire the cavity-mediated suppression or enhancement of the nonlinear response. (b) Time-resolved participation ratio normalized to the number of sites ($N=351$). Curves correspond to: the uncoupled control (black; $\Delta_B = 128$ meV); H-aggregates (red, blue; $\Delta_B = 0, 23$ meV); and J-aggregates at the baseline (green; $\Delta_B = 0$), the localization trap (purple; $\Delta_B = 120$ meV), and the resurrected resonance (gold; $\Delta_B = 240$ meV). The inset highlights the rapid spatial collapse within the localization trap at $\Delta_B = 4|J|$. The protection plateau (gold) demonstrates the recovery of collective delocalization, tracking the $J=0$ baseline. (c) Universal phase diagram for the many-body response. The boundary $\Delta_B + 4J = \Omega_R$ defines the "Many-Body Resurrection" where intrinsic molecular interactions balance cavity-induced delocalization. Regions of Spectral Starvation (harmonic regime) and Many-Body decoupling (localized regime) are indicated. Representative materials (TDBC, WSe$_2$, and R6G) are mapped along their respective tuning trajectories (dashed lines) with yellow markers identifying the optimal resonance points.