Classical Petermann Factor as a Measure of Quantum Squeezing in Photonic Time Crystals

Photonic time crystals realize a continuum of momentum-resolved SU(1,1) parametric amplifiers. We show that a classical quantity, the Petermann factor of the effective Floquet Bogoliubov de Gennes (BdG) dynamical matrix, sets the scale of their quantum noise. In stable bands it fixes the Bogoliubov mixing and hence the mean bare-photon occupation of the Floquet vacuum, while in momentum gaps it sets the photon-number prefactor and enhances the squeezing dynamics, with the Floquet growth rate setting the time scale. This converts classical measurements of mode nonorthogonality into quantitative predictions for squeezing and photon generation, and offers a compact design parameter for engineering quantum resources in two-mode BdG platforms.