We theoretically investigate a new pathway for terahertz parametric amplification, initiated by above-gap optical excitation in the candidate excitonic insulator Ta 2 NiSe 5 . 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 Ta 2 NiSe 5 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 Ta 2 NiSe 5 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 Ta 2 NiSe 5 is a gain medium which can be used to create THz amplifiers in THz communication applications.
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