Band structure theory plays an essential role in exploring physics in both solid-state systems and photonics. To the best of our knowledge, for now, all the experimental implementations of band structure measurement are stationary with a time-independent wavevector. However, allowing the band structure to vary as a function of time will lead to a much richer set of physics, such as time-reversal operation on light, super-Bloch oscillations, dynamic localization of light under a time-dependent force, dynamical classification of topological quantum phases, and spectrum control of light. To characterize such physics, it is therefore of substantial interest to directly measure dynamic band structure as well.

If an external force is applied on a one-dimensional lattice, the dynamics of a quantum particle in this system can by described by the time-dependent wavevector. It causes the wavepackets to circulate in the first Brillouin zone and to oscillate in the real space, resulting in an effect known as the Bloch oscillation. The corresponding band structure becomes time-dependent, which can be obtained by measuring the evolution of the wavevector over time. Here, we demonstrate a direct experimental measurement of the dynamic band structure in a synthetic space including the frequency axis of light, realized in a ring resonator under near-resonant dynamic modulation. This synthetic lattice exhibits the physical picture of the evolution of the wave vector reciprocal to the frequency axis in the band structure, analogous to a one-dimensional lattice under an external force. We experimentally measure the trajectories of the dynamic band structure by selectively exciting the band with a continuous wave source with its frequency scanning across the entire energy regime of the band. Our results not only provide a new perspective for exploring the dynamics in fundamental physics of solid-state and photonic systems with the concept of the synthetic dimension but also enable great capability in band structure engineering in photonics.

Figure: Trajectories of the dynamic band structure under near-resonance modulation with fixed modulation strength.

The paper has been published in Science Advances with the title “Dynamic band structure measurement in the synthetic space”.

Link：https://advances.sciencemag.org/content/7/2/eabe4335