Fig. 1: Schematic mechanism of time crystalline behaviour that leads to amplification of THz optical reflectivity following high-frequency pumping.

a An ultrafast laser pulse (0.5eV, 45 fs) photoexcites electrons through direct dipole transitions between the valence and conduction bands. The photoexcited electrons create a squeezed state of phonons through a strong electron-phonon interaction (see equation (1)). b Reflectivity amplification of pumped Ta₂NiSe₅. Fluctuations of phonons in the squeezed state oscillate at twice the phonon frequency, ω_ph, creating an effective THz Floquet medium/ Photonic time crystal. Parametric driving from the phonon oscillations can create pairs of photons at the signal and idler frequency once stimulated by the probe pulse. This enhances the reflectivity and also scatters counter-propagating light oscillating at the idler frequency. c Relative change in the reflectivity as a function of frequency subsequent to photoexcitation. The experimental results from²³ are shown at two different temperatures together with the theoretical fit which considers parametric amplification by a 9.4 THz oscillating field.