Ultra-Broad Schmidt Modes for Biphoton States Generated by SPDC in the Chirped QPM Crystals

\n In the realm of quantum optics, the manipulation and characterization of biphoton states hold significant importance for advancing quantum information processing and communication technologies. This study explores the Schmidt decomposition of ultra-broad biphoton states, revealing that most modes are fulfilled with the frequency response points, and certain modes exhibit exceptionally broad Schmidt spectra. These Schmidt modes in frequency domain are significantly reshaped and widened by a crystal at a moderate chirp-rate when pump bandwidth is about several Giga-Hertz.\n