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, $\Delta_B + 4J = \Omega_R$, linking molecular anharmonicity ($\Delta_B$) to the macroscopic Rabi splitting ($\Omega_R$) 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.