With the support from the National Natural Science Foundation of China (grants No. 11825401, 11761161003, 11921005, and 12025406), etc., Professors Jian-Wei Pan and Shuai Chen's group from University of Science and Technology of China, collaborating with Professor Xiong-Jun Liu’s group from Peking University, made great progress in the research of simulating quantum topological materials with ultracold atoms. They realized three-dimensional (3D) spin-orbit coupling with ultracold atoms for the first time, and synthesized the ideal Weyl semimetal band, which has and only has one pair of Weyl nodes. This work is published in Science on April 16th, 2021, titled “Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin-orbit coupling”. Link to the paper: https://science.sciencemag.org/content/372/6539/271 .

Weyl semimetal is an important 3D topological quantum matter. Its band contains Weyl nodes, which possess many unusual characteristics. The Weyl semimetal that has only two Weyl nodes, the ideal Weyl semimetals, is the most fundamental one in the Weyl semimetal family. Any interacting phase born of such ideal Weyl semimetal is always nontrivial. Recently, there is much progress being made in the research of Weyl semimetal, but the ideal Weyl semimetal phase is yet to be found. Thanks to the advantages of clean environment and high controllability for ultracold atom, studying quantum topological materials with it has become an active direction, for which synthesizing spin-orbit coupling is an important technology. To simulate higher dimensional topological phases, such as the Weyl semimetal, 3D spin-orbit coupling is necessary. Constructing the more complicated 3D non-abelian potentials, is a great challenge in quantum simulation with ultracold atom.

The joint group from USTC and PKU developed an elaborate optical scheme to achieve the 3D Raman potential and the 3D spin-orbit coupling, via rotating the optical lattices for 45°and locking the relative phase (figure 1). By further adjusting experimental parameters, they constructed the ideal Weyl semimetal band with only two Weyl nodes. Drawing on the experience of “virtual slicing imaging” proposed by the PKU group and G.-B Jo group from HKUST, the researchers managed to obtain the equivalent 2D spin textures along z direction, and reconstruct the 3D spin textures to identify the Weyl nodes. Further, they implemented the quench dynamics approach to extract the topological feature of the system and determine the location of the Weyl nodes. The two complementary methods agree with each other well and confirm the realization of the ideal Weyl semimetal.

This work starts the quantum simulation of Weyl topological physics that transcends the traditional condensed matter physics. It opens a new direction for exploring exotic phenomena in the Weyl physics. The experimental scheme can be generalized to fermionic systems, for the research on strongly correlated topological physics, and can generate more progress in quantum simulation with ultracold atomic systems.

Fig1: (A) The setup of 3D spin-orbit coupling. (B) The structure of 3D Raman potentials, inducing the tunneling of atomic spin flip between lattices.

Fig2: (A) Locating the two Weyl nodes by virtual slicing imaging technique. (B) Locating the two Weyl nodes by quantum quench dynamics.