Observing momentum conservation at temporal interfaces in synthetic frequency dimension

Electromagnetic wave dynamics at the temporal interface (TI), defined as the abrupt change of material properties in time, is fundamentally different from the counterpart at the spatial interface. The cornerstone for understanding the temporal scattering process for waves links to the momentum conservation for the state projections on the energy bands at the TI. Here, we experimentally construct various TIs in synthetic frequency dimension and study temporal scattering processes over the whole band. Different temporal operation scenarios are studied, including band shifting, band unfolding/folding, and also band variation in a two-dimensional case. We develop the spectral tomography method to retrieve wave function distributions after wave scatterings at different TIs and then demonstrate the momentum conservation over the whole band. Our work provides a flexible experimental platform for realizing TIs in the optical frequency range and studying the fundamental temporal scattering processes for photons.