  The duality of space and time in Maxwell's equations has prompted interest in
time boundaries and the accompanying temporal analog of spatial reflection and
refraction. However, achieving observable time boundary effects at optical
frequencies in real materials is challenging. In this work, we demonstrate that
time reflection and refraction can be observed in a two-band model centered
around a non-zero reference energy. Our model can be physically implemented in
the synthetic frequency dimension as a system of two coupled
dynamically-modulated ring resonators. We find that modulation at microwave
frequencies is sufficient to observe time boundary effects for optical waves in
synthetic frequency dimension. Our work shows that implementing multi-band
models in synthetic dimensions opens a new avenue for further exploration of
time boundaries.
