Reconfigurable high-dimensional synthetic photonic lattices.

Reconfigurable high-dimensional synthetic photonic lattices offer a promising platform for exploring the dynamic evolution of complex physical systems in high-dimensional spaces. However, the realization of reconfigurable high-dimensional synthetic lattices remains a notable challenge to date. Here, we propose a strategy for realizing dimensionally scalable temporal-domain synthetic photonic lattices, which enables independent control over both the phase and intensity of the signal light at each lattice site and time step within a high-dimensional space. By introducing multiple link rings to realize coupling between site rings, this strategy facilitates the exploration of a wide range of complex physical phenomena. We experimentally validate this proposed strategy in an optical fiber ring system, demonstrating nonreciprocal couplings up to three-dimensional space, topological funnel states, and periodic non-Hermitian temporal modulation to two-dimensional space. Moreover, we theoretically discuss the Weyl surfaces in five-dimensional space. This work provides a platform for exploring high-dimensional physics and paves the way for simulating complex systems, such as quantum many-body models.