Quantum theory of wave scattering from time interfaces

In this presentation, we shed light on electromagnetic time interfaces using the principles of quantum optics. We begin by explaining the transformation of bosonic mode operators in response to a temporal discontinuity in the macroscopic parameters. Accordingly, our discussion extends to the general analysis of photon statistics and the degree of second-order coherence of the generated forward and backward modes. Focusing on input number states, we meticulously detail the quantum states produced after the time interface, elucidating the associated probability distributions. By virtue of this study, we specifically highlight the controllable nature of photon statistics of the output forward mode for particular input states. We show that this capability, in general, is not present for the backward mode generated through the time interface. Also, we reveal that photon-pair generation is a fundamental inherent feature of the time interface. By unveiling all these insights, we aim to pave the way for exploring photonic time crystals within the domain of quantum optics.