Experimental observation of energy-band Riemann surface

Key findings from this study

• The study provides the first experimental observation of an energy-band Riemann surface using photonic synthetic frequency dimensions.
• The researchers directly measured complex-energy winding, open-boundary spectra, generalized Brillouin zones, and branch points of the Riemann surface.
• The findings establish energy-band Riemann surfaces as a unified framework explaining diverse topological effects in non-Hermitian systems.

Overview

Non-Hermitian systems that exchange energy with their environment exhibit complex energy band structures forming Riemann surfaces. These energy-band Riemann surfaces underpin topological phenomena and device applications in non-Hermitian physics. Despite theoretical development, experimental observation of such structures has remained absent. This work provides the first photonic observation of an energy-band Riemann surface through tunable imaginary gauge transformation in synthetic frequency dimensions.

Methods and approach

The researchers implemented a photonic platform utilizing synthetic frequency dimensions to access the non-Hermitian energy band structure. They employed a tunable imaginary gauge transformation to manipulate the band topology. This approach enabled direct measurement of the Riemann surface geometry and its topological properties without relying solely on theoretical calculations.

Results

Experimental measurements revealed the complete structure of the energy-band Riemann surface, including its complex-energy winding characteristics. The study identified critical topological features: the open-boundary-condition spectrum distinct from bulk properties, the generalized Brillouin zone structure in complex momentum space, and the branch points where band sheets connect. These observations confirm that the energy-band Riemann surface provides a unified description of non-Hermitian topological effects previously characterized through disparate experimental signatures.

Implications

The experimental realization of energy-band Riemann surface visualization establishes a foundational framework for understanding non-Hermitian topology. Direct access to Riemann surface geometry enables systematic investigation of how complex energies and momenta generate topological phenomena. This unified perspective consolidates diverse experimental signatures of non-Hermitian systems into a coherent geometric description. The photonic platform demonstrates that synthetic frequency dimensions provide practical avenues for exploring complex band structures otherwise inaccessible in conventional condensed matter systems.

Scope and limitations

This summary is based on the study abstract and available metadata. It does not include a full analysis of the complete paper, supplementary materials, or underlying datasets unless explicitly stated. Findings should be interpreted in the context of the original publication.