Recently, the research group of Luming Duan, Institute of Interdisciplinary Information, Tsinghua University, has made important progress in the field of quantum simulation of ion traps, using a single trapped ion to successfully realize the quantum simulation of two-dimensional Weyl particles in a magnetic field. The research paper "Quantum Simulation of the Two-Dimensional Weyl Equation in a Magnetic Field" was recently published in the international academic journal "Physical Review Letters" ).


Relativistic quantum mechanics combines two of the most important theories in modern physics: special relativity and quantum mechanics. The Weyl equation is one of the simplest relativistic quantum mechanical equations, describing zero-mass particles with spin 1/2 - Weyl fermions. As one of several elementary particles permitted by the theory of relativistic quantum mechanics, the Weyl fermion has yet to be discovered experimentally: it was once thought to describe the neutrino, but it is now known that neutrinos have tiny masses, not Zero mass particles.


Therefore, to study the properties of Weyl fermions experimentally, only by means of quantum simulation. Previous experiments have measured the energy spectrum and transport properties of Weyl fermions in photonic crystals and condensed matter systems, but have not been able to directly study their dynamics. On the other hand, quantum simulations of the dynamics of massive Dirac particles have been performed in ion trap systems, but they are limited to one-dimensional space and cannot study properties such as spin dynamics and response to magnetic fields.

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Experimental schematic
 

In this work, the researchers successfully realized the quantum simulation of the two-dimensional Weyl equation in a magnetic field by manipulating the internal state of the trapped ion and the phonon modes in two different spatial directions by laser. By preparing different initial states and measuring different spin observations, the researchers successfully verified the linear dispersion relationship of the two-dimensional Weyl particle, the discrete Landau energy level in the magnetic field, and the conservation of helicity. By introducing additional spatial and spin degrees of freedom, this work expands the application of quantum simulations to particle physics.

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Linear Dispersion Relation and

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Dynamic Evolution Measurement of Discrete Energy Levels in Magnetic Fields


The co-first authors of the paper are Jiang Yue, a 2017 doctoral student at the Institute of Interdisciplinary Information, Minglei Cai, a researcher at Huayi Boao Quantum Technology Co., Ltd. , and Yu Wu, an assistant professor at the Institute of Interdisciplinary Information. Kai, the corresponding author is Professor Duan Luming. Other authors include Mei Quanxin, a 2017 doctoral student of the Interdisciplinary Institute of Information, Zhao Wending, a 2017 doctoral student of the Interchange Institute, Chang Xiuying, an experimenter, He Li, an associate researcher, Zhou Zichao, and Yao Lin, a researcher at Huayi Boao Quantum Technology Co., Ltd. . This work was funded and supported by the Independent Research Program of Tsinghua University, the Beijing Institute of Quantum Information Science, the Frontier Science Center for Quantum Information of the Ministry of Education, and the Research Start-up Fund of Tsinghua University.


Paper link:

https://link.aps.org/doi/10.1103/PhysRevLett.128.200502