A Metamaterial Analog of the Ising Model

The interaction between microscopic particles is always a fascinating and intriguing area of science. Direct interrogation of such interactions is often difficult. Structured electromagnetic systems offer a rich toolkit for mimicking and reproducing the key dynamics that govern the microscopic interactions, and thus provides an avenue to explore and interpret the microscopic phenomena. In particular, metamaterials offer the freedom to artificially tailor light-matter coupling and to control the interaction between unit cells in the metamaterial array. Here, a terahertz metamaterial that mimics spin-related interactions of microscopic particles in a 2D lattice via complex electromagnetic multipoles scattered within the metamaterial array is demonstrated. Fano resonances featured by distinct mode properties due to strong nearest-neighbor interactions are discussed, which draw parallels with the 2D Ising model. Interestingly, a phase transition from single Fano resonance to hyperfine splitting of the Fano spectrum is observed by manipulating the 2D interactions without applying external magnetic or electric fields, which provides a potential multispectral platform for applications in super-resolution imaging, biosensing, and selective thermal emission. The dynamic approach to reproduce static interaction between microscopic particles will enable more profound significance in exploring the unknown physical world by the macroscopic analogs.