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Quantum Hall system possesses topologically protected edge states which haveenormous theoretical and practical implications in both fermionic and bosonicsystems. Harnessing the quantum Hall effect in optical platforms with lowerdimensionality is highly desirable with synthetic dimensions and has attractedbroad interests in the photonics society. Here, we introduce an alternative wayto realize the artificial magnetic field in a frequency dimension, which isachieved in a pump-probe configuration with cross-phase modulations in aone-dimensional four waveguide array. The dynamics of the topological chiraledge state has been studied and the influence from the crosstalk of the pumpfields has been explored. Our work shows an all-optical way to simulate thequantum Hall system in a photonic system and holds potential applications inmanipulating light in waveguide systems.

All-optical control of the photonic Hall lattice in a pumped waveguide array