Versatile photonic frequency synthetic dimensions using a single programmable on-chip device.

Investigating physical models with photonic synthetic dimensions has been generating great interest in vast fields of science. The rapidly developing thin-film lithium niobate (TFLN) platform, for its numerous advantages including high electro-optic coefficient and scalability, is well compatible with the realization of synthetic dimensions in the frequency together with spatial domain. While coupling resonators with fixed beam splitters is a common experimental approach, it often lacks tunability and limits coupling between adjacent lattices to sites occupying the same frequency domain positions. Here, on the contrary, we conceive the resonator arrays connected by electro-optic tunable Mach-Zehnder interferometers in our configuration instead of fixed beam splitters. By applying bias voltage and RF modulation on the interferometers, our design extends such coupling to long-range scenario and allows for continuous tuning on each coupling strength and synthetic effective magnetic flux. Therefore, our design enriches controllable coupling types that are essential for building programmable lattice networks and significantly increases versatility. As the example, we experimentally fabricate a two-resonator prototype on the TFLN platform, and on this single chip we realize well-known models including tight-binding lattices, the Hall ladder and Creutz ladder. We directly observe the band structures in the quasi-momentum space and important phenomena such as spin-momentum locking, flat band and the Aharonov-Bohm cage effect. These results demonstrate the potential for convenient simulations of more complex models in our configuration.