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Experimental observation of energy-band Riemann surface
Dali Cheng1,2, Heming Wang1,2, Janet Zhong1,3
1Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA.
Science Advances
|March 18, 2026
Summary
Researchers experimentally observed the complex energy-band Riemann surface in non-Hermitian physics. This breakthrough reveals key topological signatures and unifies diverse non-Hermitian phenomena through photonic observation.
Area of Science:
- Condensed Matter Physics
- Quantum Physics
- Photonics
Background:
- Non-Hermiticity is crucial in systems exchanging energy with their environment.
- Non-Hermitian physics exhibits unique topological phenomena and device applications.
- Complex energy bands form a Riemann surface, fundamental to non-Hermitian topology.
Purpose of the Study:
- To experimentally observe the energy-band Riemann surface in a non-Hermitian system.
- To investigate the topological properties of this Riemann surface.
- To establish a unified experimental framework for non-Hermitian topological physics.
Main Methods:
- Utilized a tunable imaginary gauge transformation in photonic synthetic frequency dimensions.
- Developed a photonic platform for observing non-Hermitian energy bands.
- Measured topological features of the energy-band Riemann surface.
Main Results:
- Provided the first experimental observation of a non-Hermitian energy-band Riemann surface.
- Revealed complex-energy winding, open-boundary spectra, generalized Brillouin zones, and branch points.
- Demonstrated the topological significance of the Riemann surface in non-Hermitian systems.
Conclusions:
- Experimental observation of energy-band Riemann surfaces offers a unified framework for non-Hermitian topological physics.
- This work bridges theoretical concepts with experimental reality in topological physics.
- Enables deeper understanding and exploration of diverse non-Hermitian phenomena.
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