Quantum Theory of Wave Scattering from Electromagnetic Time Interfaces

Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different branches of electromagnetism and optics. However, compared with the research efforts and progresses that have taken place in the realm of classical electrodynamics, the quantum aspects of this emerging subject have been less explored. Here, through the lens of quantum optics, we study the scattering of electromagnetic fields from an isotropic and nondispersive material with a suddenly changing refractive index, creating a time interface. We revisit the transformation of the bosonic mode operators and corresponding quantum states due to this interface, governed by the two-mode squeeze operator. Building on this foundation, more importantly, our analysis focuses on the photon statistics and quantum state engineering of the scattered light, elucidating various quantum optical phenomena and opportunities arising from the time interface. Notably, these include photon-pair production and destruction, photon bunching and antibunching, vacuum generation, quantum state discrimination, and quantum state freezing. To bridge theory and experiment, we propose a possible circuit quantum electrodynamics approach for validating our theoretical predictions. We hope that our work inspires experimental investigations and further quantum optical explorations of electromagnetic field interaction with photonic time crystals or with dispersive time-varying materials.