Non-Abelian Braiding with Sound and Light
Abstract – Many physics laws and mathematical rules are insensitive to order. For example, the addition of numbers disregards the sequence order, e.g., 1+2+3=3+1+2. However, such a commutative property does not always hold. When the outcomes of a set of operations depend on the execution order, they can become “non-Abelian.” In the 20th century, non-Abelian mathematical frameworks have played profound roles in formulating many fundamental laws of modern physics. Famous examples include the classification of hadrons and the unification of electro-weak interactions. Classical physics, such as mechanics, electromagnetism, and optics, were well established before non-Abelian theories came into play. However, this does not mean non-Abelian effects are absent in the classical world. One prominent example is a Rubik’s Cube—the moves made on the cube do not always commute: two sequential moves done in different orders do not necessarily get the color palettes to the same layout. We then ask: how and when non-Abelian phenomena arise in classical waves? Delving into this question, our recent works leverage Berry-phase matrices, which capture the adiabatic evolution of multiple states, to realize non-Abelian braiding in acoustics [1] and photonics [2]. Here, the braiding operations are implemented using coupled waveguide arrays, which are adiabatically modulated along the guiding direction to enforce a multi-state Berry-phase matrix that swaps the modal dwell sites. The evolution of the guiding modes maps to the generators of braid groups. The non-Abelian characteristics are revealed by switching the order of two distinct braiding operations involving at least three modes. Our results offer new perspectives in exploring novel wave-controlling schemes for future technological applications [3].
[1] Z.-G. Chen, R.-Y. Zhang, C. T. Chan, and G. Ma, Classical Non-Abelian Braiding ofAcoustic Modes, Nat. Phys. 18, 179 (2022).
[2] X.-L. Zhang, F. Yu, Z.-G. Chen, Z.-N. Tian, Q.-D. Chen, H.-B. Sun, and G. Ma, Non-Abelian Braiding on Photonic Chips, Nat. Photon. 16, 390 (2022).
[3] Y. Yang, B. Yang, G. Ma, J. Li, S. Zhang, and C. T. Chan, Non-Abelian Physics in Light and Sound, Science 383, eadf9621 (2024).
Bio – Dr. Guancong Ma is currently a professor of physics at Hong Kong Baptist University. He received B.Sc. in applied physics at the South China University of Technology in 2007 and then Ph.D. in physics at the Hong Kong University of Science and Technology in 2012. After that, he became a postdoc fellow at the Institute for Advanced Study and the Department of Physics at the same institution until 2017, when he joined the Department of Physics at Hong Kong Baptist University. He now serves as a member of the Executive Committee of the Physics Society of Hong Kong. Dr. Ma was awarded the “Young Investigator Award 2021” by the International Phononics Society, and was selected as one of the “Top 10 Rising Stars in Science and Technology 2021” by the China Association for Science and Technology. He is the recipient of the “C. N. Yang Award” in 2022, awarded by the Association of Asia Pacific Physical Societies and the Asia Pacific Center for Theoretical Physics. Dr. Ma has obtained support from the National Natural Science Foundation of China’s Excellent Young Scientists Scheme (Hong Kong & Macao). Dr. Ma’s research currently focuses on studying topological physics and non-Hermitian physics in using acousticwave and mechanical platforms. He is also interested in metamaterials and complex waves. He has published over 50 papers in peer-reviewed journals, including Science, Nature, Nature research journals, Physical Review X, Physical Review Letters. His papers have received over 9100 citations, which, according to Charivate, makes him one of the “World’s Top 2% Scientists.” Dr. Ma also holds 8 US patents, 2 WIPO patents, and 9 Chinese patents.
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