Experimental simulation of next-nearest-neighbor Heisenberg chain with photonic crystal waveguide array

Next-nearest-neighbor Heisenberg chain plays important roles in solid state physics, such as predicting exotic electric properties of two-dimensional materials or magnetic properties of organic compounds. Direct experimental studies of the many-body electron systems or spin systems associating to these materials are challenging tasks, while optical simulation provides an effective and economical way for immediate observation. Comparing with bulk optics, integrated optics are more of fascinating for steady, large scale and long-time evolution simulations. Photonic crystal is an artificial microstructure material with multiple methods to tune the propagation properties, which are essential for various simulation tasks. Here we report for the first time an experimental simulation of next-nearest-neighbor Heisenberg chain with an integrated optical chip of photonic crystal waveguide array. The use of photonic crystal enhances evanescent field thus allows coupling between next-nearest-neighbor waveguides in such a planar waveguide array, without breaking the weak coupling condition of the coupled mode equation. Particularly, similarities between the model and coherent light propagation could reach 0.99 in numerical simulations and 0.89 in experiment. Localization effect induced by second-order coupling and coupling strengthening with increasing wavelengths were also revealed in both numerical simulations and experiments. The platform proposed here is compatible with mature complementary metal oxide semiconductor technology thus possesses the potential for larger-scale problems and photonic crystals further allows simulations of specific target Hamiltonians.