Observation of spin-tensor induced topological phase transitions of triplet degenerate points with a trapped ion

We work with a three-level system in a trapped $^9\rm{Be}^+$ ion to experimentally simulate a spin-tensor-momentum topological system. We observe different types of triply degenerate points (TDPs) with different topological charge via measuring the Berry flux on a loop around the gap-closing lines, as well as the topological phase transition on the gap-closing point. For measuring the Berry flux, we explore a new method by examining the geometric rotations of both spin vectors and tensors, which differs from spin-1/2 case where Berry flux can be described solely by the rotation of spin vectors. Our work paves the way to explore novel topological phenomena. In addition, the controllable multi-level ion offers an ideal platform to study high-spin topological physics.