Quantum simulation of triplet simplex topological monopoles realized at CSU
Jiangfeng Du and Yiheng Lin at the Key Laboratory of Microscopic Magnetic Resonance, Chinese Academy of Sciences, University of Science and Technology of China (USTC), in collaboration with Hope Luo at the Key Laboratory of Quantum Information, Chinese Academy of Sciences, have made important progress in quantum simulation of topological phase transitions. By developing a tuning technique for the high-spin ion trap system, a quantum simulation of triple simplex topological monopoles has been realized, and phase transitions between monopoles with different topological charges have been observed, and the important role of the spin tensor in them has been demonstrated. The results of this study were published in Physical Review Letters on December 14, 2022 under the title "Observation of Spin-Tensor Induced Topological Phase Transitions of Triply Degenerate Points with a Trapped Ion" [Phys. Rev. Lett. 129, 250501 (2022)].
In 2016, the Nobel Prize in Physics was awarded to three scientists for their pioneering contributions to topological physics. Topology is derived from mathematics and refers to the overall properties that remain unchanged under continuous local variations. For example, the topological equivalence of a bagel and a teacup is due to the fact that they both have a hole through which they penetrate, and the number of holes is a topological property that corresponds to the topological charge. Scientists have found that topology also plays a key role in condensing some physical properties of matter that do not depend on the details of the sample and are determined entirely by the overall topological nature of the system state. And topological phase transitions - transitions between states with different topological properties - must be discontinuous jumps. For example, in some semimetallic materials, monopole-like topologies formed by energy band simplex points can have different topological charges, and exploring the topological phase transition between them is one of the current frontier research directions. At the same time, quasiparticle excitations near the simple merger point exhibit elementary particle-like behavior, and exploring their topological phase transitions is also important for exploring new types of particles.
In this study, experimental simulations are carried out for an important class of fermions in topological phase transitions, the triple simplex fermion model. This model corresponds to topological monopoles with spin 1 and has received much attention in recent studies. However, direct observation of the topological phase transition of such triple simplexes in solid material systems requires complex modulation and is currently difficult to achieve. Therefore, highly controllable quantum simulators offer a new way to study topological phenomena. In this study, the behavior of topological monopoles with spin 1 can be effectively observed by using beryllium ions bound in an ultra-high vacuum environment, combined with precise tuning by microwaves and radio frequency to construct a multi-energy quantum system. By tuning 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 in it (shown in Figure 1). The highly tunable multi-energy bound ion system developed in this work provides a good platform for studying high spin physics and paves the way for further studies of novel high-order topological simplex states as well as other topological monopole phenomena.
Figure 1. Experimental results of topological quantum simulation with spin 1. Left: Experimentally observed topological phase transition behavior, where β>-2 corresponds to a topological charge of 2 and β<-2 corresponds to a topological charge of 0. The data in different colors represent the contributions of various components in the topological phase transition, where the yellow data represent the contribution of the tensor part and the solid line is the corresponding theoretical prediction. Right: Experimental observation of the geometric wrapping behavior of the tensor ellipsoid near the topological phase transition point β≈-2. The evolution of the spin tensor ellipsoid in a specific loop in the parameter space can clearly reflect the tensor contribution to the topological charge.
The ion trap experimental system used in the study belongs to the high spin quantum simulators that have been rapidly developed in recent years. Academician Jiangfeng Du and Professor Yiheng Lin at the Key Laboratory of Microscopic Magnetic Resonance, CAS, led a team to build the experimental platform from scratch and successfully developed a series of novel high-spin manipulation techniques, including the use of kinetic decoupling to increase the three-energy state coherence time by an order of magnitude [Phys. Rev. A. 106, 022412 (2022)]; shape pulses assisted by an analytical model to achieve a four-energy system with two near-neighbor leaps The above work provides the basis for the present study. The above work lays the core experimental foundation for the research in this paper. Prof. Hope Luo from the Key Laboratory of Quantum Information, CAS, and Prof. Chuanwei Zhang from the University of Texas at Dallas provided the core theoretical support for the work in this paper.
The reviewers highly praised 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, the spin-tensor-momentum-coupling could be generated for spin-1 systems, leading to intriguing quantum phenomena different from spin-1/2 ones. This work is interesting and important.")
Mengxiang Zhang and Yue Li, PhD students at the Key Laboratory of Microscopic Magnetic Resonance, CAS, and Xinxing Yuan, PhD, are co-first authors of the paper, and Jiangfeng Du, Prof. Yiheng Lin, and Prof. Hope Luo are co-corresponding authors. This research was supported by the National Natural Science Foundation of China, the Chinese Academy of Sciences, the Ministry of Science and Technology, and Anhui Province.
Links to the paper:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.250501
