Recently, the research team led by Professor Li Chaohong from the College of Physics and Optoelectronic Engineering and the Institute of Quantum Precision Measurement at Shenzhen University proposed the theory of topological inverse band based on the waveguide quantum electrodynamics system, revealing the topological-dependent photon scattering. The relevant findings were published on September 8, 2023, in the prestigious physics journal "Physical Review Letters" [https://doi.org/10.1103/PhysRevLett.131.103604].

Band theory is a cornerstone of condensed matter physics. Under the influence of periodic lattice potentials, the energy of electrons varies continuously with the lattice momentum, forming energy bands. Energy band gaps determine whether a material is a conductor, semiconductor, or insulator. For a long time, attention was focused on the energy of the bands, neglecting the overall phase of electron Bloch states within the bands. 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 the topological phase of quantum states. Utilizing topological band theory, researchers have predicted and discovered novel topological quantum states, such as topological insulators, topological semimetals, and topological magnetic materials, making it a powerful tool for studying topological quantum states.

In recent years, researchers have been exploring how to design and control the behavior of light using topological properties, leading to the development of the frontier field of topological photonics. Early research in topological photonics mainly focused on simulating topological models and quantum states from condensed matter physics. Due to the unique properties of photonic systems, they can go beyond simple simulations of topological quantum states. For example, adding gain to a photonic topological insulator can realize a topological insulator laser, which exhibits superior characteristics such as monochromaticity, emission efficiency, and stability. Understanding the influence of topological properties on the interaction between light and atoms will pave the way for the development of topologically protected photonic devices, quantum communication, and quantum information processing. The waveguide quantum electrodynamics system [Fig. (a)] is a hybrid quantum system coupling waveguides with atoms, possessing strong light-matter interactions, 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 [Fig. (b)], rendering the conventional 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 conventional topological band theory in waveguide quantum electrodynamics systems, Professor Li Chaohong's team first proposed that the reciprocal of energy varies continuously with lattice momentum to form continuous inverse bands [Fig. (c)], and revealed the relationship between the topological phase in the inverse bands and photon scattering. By calculating the topological Berry phase of the inverse bands, they discovered a topological phase transition determined by the incident photon frequency, contrasting sharply with the topological phase determined by the electronic material structure in condensed matter physics. The team found that the system exhibits flat bands and dark Weyl states supported by the flat bands. Due to the absence of frequency shifts, dark Weyl states have ultra-long lifetimes and ultra-narrow linewidths, making them suitable for quantum information storage and precise frequency measurement. Because the waveguide quantum electrodynamics system suffers from radiation decay, even in the case of nontrivial topology, there are no topological edge states at the boundary. However, the team discovered a unique bulk-edge correspondence in this system. In the case of nontrivial topology, scale-invariant localized states are distributed in a single inverse band, while in the case of trivial topology, scale-invariant localized states are distributed in two inverse bands. Perhaps one of the most surprising findings is that the winding number of photon scattering depends not only on the topological phase of one inverse band but also on the parity of the unit number. These results reveal the rich and complex topological quantum states in waveguide quantum electrodynamics systems, inspiring further research into the topological behavior of light-matter interactions.

The achievement, titled "Topological Inverse Band Theory in Waveguide Quantum Electrodynamics," was published in "Physical Review Letters." Shenzhen University served as the first institution and corresponding institution, with Dr. Ke Yongguan (Associate Professor at Sun Yat-sen University and Visiting Scholar at Shenzhen University) as the first author, and Professor Li Chaohong and Professor Yuri Kivshar (Professor at the Australian National University and Honorary Professor at Shenzhen University) as co-corresponding authors. The research was supported by the National Key R&D Program, the National Natural Science Foundation of China, and key research and development projects in Guangdong Province. Since joining Shenzhen University in 2022, Professor Li Chaohong's team has made gratifying progress in innovative research and talent introduction in research areas such as quantum engineering and artificial quantum systems, quantum correlations and novel quantum states, and quantum precision measurement and quantum sensor devices, establishing the "Shenzhen University Institute of Quantum Precision Measurement" relying on the College 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 of bound state topological transport and topological resonant tunneling by Professor Li Chaohong's team in 2017 [Phys. Rev. A 95, 063630 (2017)] was recently experimentally confirmed by the group of Professor Esslinger at ETH Zurich, with their experimental results published in "Nature Physics" [https://doi.org/10.1038/s41567-023-02145-w]. Dr. Ke Yongguan and Professor Li Chaohong were invited to write a review for "Nature Physics" [https://doi.org/10.1038/s41567-023-02169-2].