Extreme Terahertz Nonlinear Phononics by Coherence-Imprinted Control of Hybrid Order

Coherent control of quantum materials has progressed along two major fronts: nonlinear phononics, which reshapes lattices to induce emergent states, and Floquet engineering, which tailors electronic band reconstruction via time-periodic driving. Both mechanisms face fundamental limitations at terahertz (THz) frequencies: phononic nonlinearities are intrinsically weak in standard lattices, while electronic Floquet states are often constrained by rapid decoherence upon light-off and by a scarcity of coherence-resolved, multi-correlation probes beyond (quasi-)stationary band structures. Here we report an extreme THz nonlinear-phononics mechanism in $\text{Ta}_\text{2}\text{NiSe}_\text{5}$, where a highly susceptible non-equilibrium electronic correlation bath dramatically amplifies lattice nonlinearities under coherent driving. Utilizing THz two-dimensional spectroscopy as a coherence-tomography tool, we resolve an exceptionally rich landscape of approximately 30 distinct multi-order quantum pathways, including high-harmonic phonon generation, multi-quantum coherences, and multi-wave anharmonic cross-mode mixing. The density and complexity of this extreme manifold establishes a new benchmark for THz nonlinear phononics, as the multi-order quantum pathways surpass the limits of conventional lattice responses. These high-order signals collapse above ~100~K, defining an electronic correlation scale of a coherence-imprinted hybrid electronic-phonon order that governs the sustainability of high-order quantum correlations and nonlinear pathways beyond linear and equilibrium responses. Our results establish a route for correlation-boosted, phonon-anchored periodic Hamiltonian engineering and for certifying such periodically-driven states via multi-correlation coherence tomography.