Du Jiangfeng, Lin Yiheng et al., CAS Key Laboratory of Micromagnetic resonance, University of Science and Technology of China, and Luo Hope et al., CAS Key Laboratory of Quantum Information, have made important progress in the quantum simulation of topological phase transitions. The quantum simulation of a triple degenerate topological monopole with different topological charges has been achieved by developing the regulation technique of a high spin ion trap system. The phase transition between monopoles with different topological charges has been observed, and the important role of the spin tensor has been demonstrated. The findings were published on December 14, 2022 under the title "Observation of Spin-Tensor Induced Topological Phase Transitions of Triply Degenerate Points with a Trapped Ion "in Physical Review Letters [Phys. Rev. Lett. 129, 250501 (2022)].

Topological state is one of the frontier and mainstream fields of current physics research, which brings new ideas for the design of new materials and new devices, and even has important significance for our in-depth understanding of the properties of fundamental particles in the universe. In 2016, the Nobel Prize in Physics was awarded to three scientists for their groundbreaking contributions to topological physics. Topology, derived from mathematics, refers to global properties that remain constant under continuous changes in local areas. For example, bagels and teacups are topologically equivalent because they both have a penetrating hole, and the number of holes is a topological property corresponding to the topological charge. The scientists found that topology also plays a key role in some physical properties of condensed matter that do not depend on the details of the sample, but are determined entirely by the overall topological properties of the system state. And topological phase transitions - transitions between states with different topological properties - must be discontinuous jumps. For example, in some semi-metallic materials, monopole like topologies formed by band degeneracy points can have different topological charges, and the exploration of topological phase transitions between them is one of the frontiers of current research. At the same time, the excitation of quasiparticles near the degeneracy point shows a behavior similar to that of elementary particles, and the exploration of topological phase transitions is also of great significance for the exploration of new particles.

In this study, an important class of fermion models in topological phase transitions, the triple degenerate fermion model, is experimentally simulated. This model corresponds to a topological monopole with spin 1, and has received extensive attention in recent studies. However, the direct observation of topological phase transitions of such triple degeneracy points in solid material systems requires complex regulation and is difficult to achieve at present. Therefore, highly controllable quantum simulators provide a new way to study topological phenomena. In this study, by using beryllium ions bound in ultra-high vacuum environment, combined with the quasi-regulation of microwave, radio frequency, etc., to construct a multi-level quantum system, it is possible to effectively observe the behavior of topological monopole with spin 1. By manipulating the experimental parameters, the researchers clearly observed the topological phase transition of the quantum state and extracted the contribution of the higher-order spin tensor to it (Figure 1). The highly regulated multilevel bound ion system developed in this work provides a good platform for the study of high spin physics, and paves the way for further study of novel higher-order topological degeneracy and other topological monopole phenomena.

FIG. 1. Results of topological quantum simulation experiment with spin 1. Left: the observed topological phase transition behavior, where β>-2 corresponds to a topological charge of 2, β<-2 corresponds to a topological charge of 0; The different colors of the data represent the contributions of the various components of the topological phase transition, where the yellow data represents the contributions of the tensor portion, and the solid lines represent the corresponding theoretical predictions. Right: Experimental observation of the geometric circling behavior of the tensor ellipsoid near the topological phase transition point β≈-2. The evolution of the spin tensor ellipsoid in a particular loop in the parameter space can clearly reflect the contribution of the tensor to the topological charge.

The ion trap experimental system used in this study belongs to the high-spin quantum simulator developed rapidly in recent years. Academician Du Jiangfeng and Professor Lin Yiheng led the team of CAS Key Laboratory of Micromagnetic Resonance to build an experimental platform from scratch and successfully develop a series of new high-spin control technologies. Including the use of dynamic decoupling to improve the coherence time of three-level states by an order of magnitude [Phys. Rev. A. 106, 022412 (2022)]; Rapid universal regulation between two nearest neighbor transitions of a four-level system is realized by analytical model-assisted shape pulses [Phys. Rev. Applied. 18, 034047 (2022)]. The above work has laid the core experimental foundation for the research of this paper. The Key Laboratory of Quantum Information of the Chinese Academy of Sciences, Prof. Hope Luo, and the University of Texas at Dallas, Prof. Chuanwei Zhang, provide the core theoretical support for this work.

The reviewer spoke highly of the work, noting that "... importantly,  the spin-tensor-momentum-coupling could be generated for spin-1 systems and induce intriguing quantum phenomena  different from spin-1/2 ones. This work is of interest and importance. "("... Importantly, spin-tensor-momentum coupling can be generated by systems with spin 1, leading to interesting quantum phenomena that differ from spin 1/2. This work is interesting and important." )

Zhang Mengxiang, Li Yue and Yuan Xinxing, PhD students at the CAS Key Laboratory of Micromagnetic resonance, are co-first authors of the paper, and Du Jiangfeng, Academician, Lin Yiheng and Luo Xixing are co-corresponding authors. The research was funded by the National Natural Science Foundation of China, the Chinese Academy of Sciences, the Ministry of Science and Technology, and Anhui Province.

Paper link：https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.250501

(Key Laboratory of Micromagnetic Resonance of Chinese Academy of Sciences, Key Laboratory of Quantum Information of Chinese Academy of Sciences, School of Physics, Institute of Quantum Information and Quantum Technology Innovation, Scientific Research Department of Chinese Academy of Sciences)

Source: China University of Science and Technology News