  Condensates are a hallmark of emergence in quantum materials with
superconductors and charge density wave as prominent examples. An excitonic
insulator (EI) is an intriguing addition to this library, exhibiting
spontaneous condensation of electron-hole pairs. However, condensate
observables can be obscured through parasitic coupling to the lattice.
Time-resolved terahertz (THz) spectroscopy can disentangle such obscurants
through measurement of the quantum dynamics. We target $Ta_{2}NiSe_{5}$, a
putative room-temperature EI where electron-lattice coupling dominates the
structural transition ($T_{c}$=326 K), hindering identification of excitonic
correlations. A pronounced increase in the THz reflectivity manifests following
photoexcitation and exhibits a BEC-like temperature dependence. This occurs
well below the $T_{c}$, suggesting a novel approach to monitor exciton
condensate dynamics. Nonetheless, dynamic condensate-phonon coupling remains as
evidenced by peaks in the enhanced reflectivity spectrum at select
infrared-active phonon frequencies. This indicates that parametric reflectivity
enhancement arises from phonon squeezing, validated using Fresnel-Floquet
theory and density functional calculations. Our results highlight that coherent
dynamics can drive parametric stimulated emission with concomitant
possibilities, including entangled THz photon generation.
