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We theoretically investigate photonic time-crystalline behaviour initiated byoptical excitation above the electronic gap of the excitonic insulatorcandidate $\rm{Ta_2 Ni Se_5}$. We show that after electron photoexcitation,electron-phonon coupling leads to an unconventional squeezed phonon state,characterised by periodic oscillations of phonon fluctuations. Squeezingoscillations lead to photonic time crystalline behaviour. The key signature ofthe photonic time crystalline behaviour is THz amplification of reflectivity ina narrow frequency band. The theory is supported by experimental results on$\rm{Ta_2 Ni Se_5}$ where photoexcitation with short pulses leads to enhancedterahertz reflectivity with the predicted features. We explain the keymechanism leading to THz amplification in terms of a simplified Hamiltonianwhose validity is supported by ab-initio DFT calculations. Our theory suggeststhat the pumped $\rm{Ta_2 Ni Se_5}$ is a gain medium, demonstrating thatsqueezed phonon noise may be used to create THz amplifiers in THz communicationapplications.

Theory of time-crystalline behaviour mediated by phonon squeezing in Ta2NiSe5