Experimental realization of the topological Haldane model with ultracold fermions

The Haldane model, which predicts complex topological states of matter, has been implemented by placing ultracold atoms in a tunable optical lattice that was deformed and shaken. Lab demonstrations of the topological Haldane model The quantum Hall effect leads to topologically protected edge states, and for a long time was thought to exclusively emerge in the presence of an external magnetic field. But in 1988, Duncan Haldane proposed a model in which this exotic electronics structure arises without this requirement. He proposed that, in a honeycomb lattice with a staggered flux, the necessary ingredients for a quantum Hall effect would be inherent in the material itself. The principles behind this concept were later recruited to design topological insulators, but in its original expression, the Haldane model has not been observed in the laboratory. In this issue of Nature , two groups report on progress connected to the Haldane model. Gregor Jotzu et al . report the first realization of the Haldane model and Pedram Roushan et al . show how it can be precisely measured. Jotzu et al . use ultracold fermions to realize the breaking of time-reversal and inversion symmetry — the two main requirements of the model — by implementing a circular modulation of the lattice position and an energy offset between neighbouring sites. Roushan et al . use superconducting quantum circuits — a Josephson junction sandwiched between superconducting electrodes — to realize a non-interacting form of the Haldane model with a single qubit and an interacting two-qubit model through a new experimental setup called 'gmon' coupling architecture. Their setup allows them to characterize both cases by measuring the Berry curvature, a feature that all topological structures have in common. The Haldane model on a honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter 1 . It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band structure, rather than being caused by an external magnetic field 2 . Although physical implementation has been considered unlikely, the Haldane model has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors 2 , 3 , 4 , 5 , 6 . Here we report the experimental realization of the Haldane model and the characterization of its topological band structure, using ultracold fermionic atoms in a peri