### Abstract: Breakthrough in PT Symmetry and Linewidth Narrowing by Liu Yongchun's Research Group at Tsinghua University Recently, the research group led by Associate Professor Liu Yongchun from the Department of Physics at Tsinghua University has made significant progress in the field of Parity-Time (PT) symmetry and linewidth narrowing. Their study, titled "PT-Symmetric Feedback Induced Linewidth Narrowing," was published in the prestigious journal *Physical Review Letters*. #### Key Events and Findings: 1. **Introduction of PT Symmetry in a Single Resonant Mode:** - The research team developed a novel method to construct a PT-symmetric system in a single resonant mode using feedback mechanisms. - This breakthrough is particularly important because previous methods required at least two resonant modes, making it infeasible to achieve PT symmetry in systems with only one resonant mode. 2. **Significance of Narrow Linewidth:** - The linewidth is a critical parameter that determines the performance of resonant systems, such as atomic ensembles, optical cavities, and mechanical oscillators. - In precision measurement and sensing applications, narrower linewidths result in sharper resonance peaks, enabling the detection of weaker signals and enhancing measurement sensitivity. 3. **Methodology:** - The team utilized two orthogonal components within a single resonant mode. - By implementing a measurement-feedback loop, they detected and fed back information from one of the orthogonal components (Px), introducing equivalent gain. - This process broke the symmetry between the two orthogonal components (Px and Py), effectively creating a PT-symmetric system. 4. **Experimental Demonstration:** - The PT-symmetric feedback scheme was demonstrated using a thermal atomic ensemble. - Circularly polarized light was used to polarize the atomic ensemble's spin, which then precessed around a magnetic field in the z-direction. - The orthogonal spin components (Px and Py) in the xy-plane formed a dissipative resonant mode. - The orthogonal component Px was measured using the paramagnetic Faraday rotation effect of probe light passing through the polarized atomic ensemble. - The feedback information was loaded onto a feedback magnetic field coil, which applied a feedback magnetic field to the atomic ensemble, introducing gain to the Px component and breaking the symmetry between Px and Py. 5. **Results:** - In the PT-symmetric region, the system's linewidth was successfully narrowed from 654 Hz to 13.6 Hz, achieving a 48-fold reduction. - This linewidth narrowing translated into a 22-fold enhancement in magnetic field measurement sensitivity. 6. **Broader Implications:** - The proposed method offers a universal approach to constructing PT-symmetric systems in single resonant modes. - This innovation paves the way for studying non-Hermitian physics in single resonant systems and has potential applications in precision measurement and sensing technologies. #### Key People and Institutions: - **First Author:** Tang Yuanjiang, a 2019 PhD student at Tsinghua University's Department of Physics. - **Corresponding Author:** Liu Yongchun, Associate Professor at Tsinghua University's Department of Physics. - **Institutions and Funding:** - Tsinghua University, Department of Physics. - National Natural Science Foundation of China. - Ministry of Science and Technology. - State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University. - Quantum Information Frontier Science Center, Tsinghua University. - Guangdong Provincial Department of Science and Technology. #### Figures and Diagrams: - **Figure 1:** Illustrates the principle of PT-symmetric feedback. - (a) Phase diagram of a typical dissipative resonant system. - (b) Schematic of the PT-symmetric feedback system. - (c) Phase diagram comparison between PT-symmetric and Hermitian systems. - (d)-(e) Real and imaginary parts of the system's eigenvalues as a function of feedback coefficient. - (f)-(g) Time evolution of the orthogonal components in the PT-symmetric and broken regions. - **Figure 2:** Schematic of the experimental setup for the thermal atomic ensemble. - **Figure 3:** Experimental results showing how linewidth and equivalent relaxation time vary with feedback coefficient. #### Conclusion: The research conducted by Liu Yongchun's group at Tsinghua University represents a significant advancement in the manipulation of resonant systems through PT symmetry. By achieving linewidth narrowing in a single resonant mode, the team has opened new avenues for enhancing precision measurement and sensing technologies. This work not only contributes to the theoretical understanding of non-Hermitian physics but also has practical implications for various scientific and technological applications.