Recently, Professor Li Zhaohong's team from the School of Physics and Optoelectronic Engineering and the Institute of Quantum Precision Measurement at Shenzhen University proposed the theory of topological anti-energy bands based on the waveguide quantum electrodynamics system. They revealed topology-dependent photon scattering. The related findings were published on September 8, 2023, in the top-tier international physics journal "Physical Review Letters". [https://doi.org/10.1103/PhysRevLett.131.103604].

The band theory is an important cornerstone of condensed matter physics. Under the influence of periodic lattice potentials, the energy of electrons varies continuously with lattice momentum, forming energy bands. There exist band gaps between these bands, the size of which determines whether a material is a conductor, semiconductor, or insulator. For a long time, attention was focused on the energy of the bands, while the overall phase of electrons in the Bloch states within the bands was overlooked. It wasn't until Thouless used Bloch states to define topological invariants to explain the integer quantum Hall effect that people began to realize the crucial role of topological phases in quantum states. Using topological band theory, people have predicted and discovered novel topological quantum states such as topological insulators, topological semimetals, and topological magnetic materials. Topological band theory has become a powerful tool for studying topological quantum states.

In recent years, researchers have been studying how to utilize topological properties to design and control the behavior of light, gradually developing the emerging field of topological photonics. Early research in topological photonics mainly focused on simulating topological models and states of matter in condensed matter physics. Due to the unique properties of photon systems, they can go beyond simple simulations of topological quantum states. For example, adding gain to a photonic topological insulator can achieve a topological insulator laser, which exhibits superior monochromaticity, luminescence efficiency, and stability. Understanding the effects of topological properties on the interaction between light and atoms will pave the way for the development of topologically protected photonic quantum devices, quantum communication, and quantum information processing. The waveguide quantum electrodynamics system [Figure (a)] is a hybrid quantum system coupling waveguides and atoms, with strong interactions between light and atoms, making it an ideal platform for studying quantum topological states and photon scattering. However, in the waveguide quantum electrodynamics system, due to the presence of photon scattering, the corresponding energy bands split into two discontinuous branches [Figure (b)], rendering the topological band theory inapplicable. Developing new theories to study topological quantum states in waveguide quantum electrodynamics systems has become an urgent need.

To address the failure of topological band theory in waveguide quantum electrodynamics systems, Professor Li Zhaohong's team first proposed that the reciprocal of energy varies continuously with lattice momentum, forming continuous anti-bands [Figure (c)], and revealed the relationship between topological phases in anti-bands and photon scattering. By calculating the topological Berry phase of anti-bands, they discovered a topological phase transition determined by the incident photon frequency, contrasting sharply with the topological phases determined by the electronic material structure in condensed matter physics. Professor Li Zhaohong's team found that this system exhibits flat bands and dark Weyl states supported by flat bands. Because dark Weyl states do not undergo frequency shifts and have ultra-long lifetimes and ultra-narrow linewidths, they can be used for quantum information storage and precise frequency measurement. Due to radiation decay in waveguide quantum electrodynamics systems, there are no topological edge states even in topologically nontrivial cases. However, Professor Li Zhaohong's team discovered a unique correspondence between bulk and boundary in this system. In the case of topologically nontriviality, scale-invariant local states are distributed in a single anti-band, while in the case of topological triviality, scale-invariant local states are distributed in two anti-bands. One of the most surprising findings is that the entanglement number of photon scattering depends not only on the topological phase of one anti-band but also on the parity of the unit number. These results reveal rich and complex topological quantum states in waveguide quantum electrodynamics systems, inspiring further research into topological behaviors in the interaction between light and matter.

This achievement, entitled "Topological Inverse Band Theory in Waveguide Quantum Electrodynamics," was published in Physical Review Letters. Shenzhen University is the first and corresponding institution, with Ke Yongguan [Associate Professor at Sun Yat-sen University, Visiting Scholar at Shenzhen University] as the first author, and Professor Li Zhaohong and Professor Yuri Kivshar [Professor at Australian National University, Honorary Professor at Shenzhen University] as co-corresponding authors. This research was supported by the National Key R&D Program, the National Natural Science Foundation of China, and key R&D projects in Guangdong Province, among others. Since joining Shenzhen University in 2022, Professor Li Zhaohong's team has made gratifying progress in innovative research and talent introduction in research directions such as quantum engineering and artificial quantum systems, quantum correlations and novel quantum states, and quantum precision measurement and quantum sensor devices, relying on the establishment of the "Shenzhen University Institute of Quantum Precision Measurement" in the School of Physics and Optoelectronic Engineering and participating in the construction of the "Guangdong-Hong Kong-Macao Greater Bay Area Quantum Science Center." Additionally, it is worth mentioning that the prediction made by Professor Li Zhaohong's team in 2017 regarding bound-state topological transport and topological resonance tunneling [Phys. Rev. A 95, 063630 (2017)] was recently experimentally verified by Professor Esslinger's group at ETH Zurich, with their experimental results published in Nature Physics [https://doi.org/10.1038/s41567-023-02145-w]. Associate Professor Ke Yongguan and Professor Li Zhaohong were invited to write a review for Nature Physics [https://doi.org/10.1038/s41567-023-02169-2].