Strong long-wavelength electron-phonon coupling in Ta$_2$Ni(Se,S)$_5$

The search for intrinsic excitonic insulators (EI) has long been confounded by coexisting electron-phonon coupling in bulk materials. Although the ground state of an EI may be difficult to differentiate from density-wave orders or other structural instabilities, excited states offer distinctive signatures. One way to provide clarity is to directly inspect the phonon spectral function for long wavelength broadening due to phonon interaction with the high velocity EI phason. Here, we report that the quasi-one-dimensional (quasi-1D) EI candidate Ta$_2$NiSe$_5$ shows extremely anisotropic phonon broadening and softening in the semimetallic normal state. In contrast, such a behavior is completely absent in the broken symmetry state of Ta$_2$NiSe$_5$ and in the isostructural Ta$_2$NiS$_5$, where the latter has a fully gapped normal state. By contrasting the expected phonon lifetimes in the BCS and BEC limits of a putative EI, our results suggest that the phase transition in Ta$_2$Ni(Se,S)$_5$ family is closely related to strong interband electron-phonon coupling. We experimentally determine the dimensionless coupling $\frac{g}{\omega_0}\sim10$, showing Ta$_2$Ni(Se,S)$_5$ as a rare "ultra-strong coupling" material.