  We theoretically investigate photonic time-crystalline behaviour initiated by
optical excitation above the electronic gap of the excitonic insulator
candidate $\rm{Ta_2 Ni Se_5}$. We show that after electron photoexcitation,
electron-phonon coupling leads to an unconventional squeezed phonon state,
characterised by periodic oscillations of phonon fluctuations. Squeezing
oscillations lead to photonic time crystalline behaviour. The key signature of
the photonic time crystalline behaviour is THz amplification of reflectivity in
a narrow frequency band. The theory is supported by experimental results on
$\rm{Ta_2 Ni Se_5}$ where photoexcitation with short pulses leads to enhanced
terahertz reflectivity with the predicted features. We explain the key
mechanism leading to THz amplification in terms of a simplified Hamiltonian
whose validity is supported by ab-initio DFT calculations. Our theory suggests
that the pumped $\rm{Ta_2 Ni Se_5}$ is a gain medium, demonstrating that
squeezed phonon noise may be used to create THz amplifiers in THz communication
applications.
