All-Optical Control of the Photonic Hall Lattice in a Pumped Waveguide Array

Quantum Hall system possesses topologically protected edge states which have\nenormous theoretical and practical implications in both fermionic and bosonic\nsystems. Harnessing the quantum Hall effect in optical platforms with lower\ndimensionality is highly desirable with synthetic dimensions and has attracted\nbroad interests in the photonics society. Here, we introduce an alternative way\nto realize the artificial magnetic field in a frequency dimension, which is\nachieved in a pump-probe configuration with cross-phase modulations in a\none-dimensional four waveguide array. The dynamics of the topological chiral\nedge state has been studied and the influence from the crosstalk of the pump\nfields has been explored. Our work shows an all-optical way to simulate the\nquantum Hall system in a photonic system and holds potential applications in\nmanipulating light in waveguide systems.\n