article published yes Dali Cheng author Heming Wang author Janet Zhong author Eran Lustig author Charles Roques-Carmes author e2e68fc9-6505-11ef-a541-eb4e72cc3e82 Shanhui Fan author Non-Hermiticity naturally arises in physical systems that exchange energy with their environment. The presence of non-Hermiticity leads to many topological physics phenomena and device applications. In the non-Hermitian energy band theory, the foundation of these physics and applications, both energies and wave vectors take complex values. The energy bands thus become a Riemann surface, and such an energy-band Riemann surface underlies all important signatures of non-Hermitian topology. Despite a long history and recent theoretical interests, the energy-band Riemann surface has not been experimentally studied. Here, we provide a photonic observation of the energy-band Riemann surface of a non-Hermitian system. This is achieved by a tunable imaginary gauge transformation in photonic synthetic frequency dimensions. From measured topologies of the Riemann surface, we reveal the complex-energy winding, the open-boundary-condition spectrum, the generalized Brillouin zone, and the branch points. Our findings demonstrate a unified framework in the studies of diverse effects in non-Hermitian topological physics through an experimental observation of energy-band Riemann surfaces. American Association for the Advancement of Science2026 eng 2375-2548 2510.0881910.1126/sciadv.aec8239 1212 yes D. Cheng, H. Wang, J. Zhong, E. Lustig, C. Roques-Carmes, and S. Fan, “Experimental observation of energy-band Riemann surface,” <i>Science Advances</i>, vol. 12, no. 12. American Association for the Advancement of Science, 2026. Cheng, Dali, Heming Wang, Janet Zhong, Eran Lustig, Charles Roques-Carmes, and Shanhui Fan. “Experimental Observation of Energy-Band Riemann Surface.” <i>Science Advances</i>. American Association for the Advancement of Science, 2026. <a href="https://doi.org/10.1126/sciadv.aec8239">https://doi.org/10.1126/sciadv.aec8239</a>. Cheng D, Wang H, Zhong J, Lustig E, Roques-Carmes C, Fan S. 2026. Experimental observation of energy-band Riemann surface. Science Advances. 12(12), eaec8239. D. Cheng, H. Wang, J. Zhong, E. Lustig, C. Roques-Carmes, S. Fan, Science Advances 12 (2026). Cheng D, Wang H, Zhong J, Lustig E, Roques-Carmes C, Fan S. Experimental observation of energy-band Riemann surface. <i>Science Advances</i>. 2026;12(12). doi:<a href="https://doi.org/10.1126/sciadv.aec8239">10.1126/sciadv.aec8239</a> Cheng, D., Wang, H., Zhong, J., Lustig, E., Roques-Carmes, C., &#38; Fan, S. (2026). Experimental observation of energy-band Riemann surface. <i>Science Advances</i>. American Association for the Advancement of Science. <a href="https://doi.org/10.1126/sciadv.aec8239">https://doi.org/10.1126/sciadv.aec8239</a> Cheng, Dali, et al. “Experimental Observation of Energy-Band Riemann Surface.” <i>Science Advances</i>, vol. 12, no. 12, eaec8239, American Association for the Advancement of Science, 2026, doi:<a href="https://doi.org/10.1126/sciadv.aec8239">10.1126/sciadv.aec8239</a>. 215832026-03-30T12:22:48Z2026-04-27T10:01:35Z