Photonic time-crystalline behaviour mediated by phonon squeezing in Ta 2 NiSe 5 .

Photonic time crystals refer to materials whose dielectric properties are periodic in time, analogous to a photonic crystal whose dielectric properties is periodic in space. Here, we theoretically investigate photonic time-crystalline behaviour initiated by optical excitation above the electronic gap of the excitonic insulator candidate Ta2 NiSe5 . 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 terahertz (THz) amplification of reflectivity in a narrow frequency band. The theory is supported by experimental results on Ta2 NiSe5 where photoexcitation with short pulses leads to enhanced THz reflectivity with the predicted features. We explain the key mechanism leading to THz amplification in terms of a simplified electron-phonon Hamiltonian motivated by ab-initio DFT calculations. Our theory suggests that the pumped Ta2 NiSe5 is a gain medium, demonstrating that squeezed phonon noise may be used to create THz amplifiers in THz communication applications.