We theoretically investigate a new pathway for terahertz parametric amplification, initiated by above-gap optical excitation in the candidate excitonic insulator Ta2NiSe5. We show that after electron photoexcitation, electron-phonon coupling can lead to THz parametric amplification, mediated by squeezed oscillations of the strongly coupled phonon. The developed theory is supported by experimental results on Ta2NiSe5 where photoexcitation with short pulses leads to enhanced terahertz reflectivity. We explain the key mechanism leading to parametric amplification in terms of a simplified Hamiltonian and demonstrate the validity of the simplified model in Ta2NiSe5 using DFT ab-initio calculations. We identify a unique 4.7 THz infrared active phonon that is preferentially coupled to the electronic bandstructure, providing a dominant contribution to the low frequency terahertz amplification. Moreover, we show that the electron-phonon coupling is strongly dependent on the order parameter. Our theory suggests that the pumped Ta2NiSe5 is a gain medium which can be used to create THz amplifiers in THz communication applications.
Main: 24 pages, 2 figures. Supplementary: 8 pages, 3 figures, 2 tables