Work

Detecting complex-energy braiding topology in a dissipative atomic simulator with transformer-based geometric tomography

Year: 2026

Type: article

Abstract: Machine learning (ML) is shaping our exploration of topological matter, whose existence is inherently tied to the geometry of quantum states or energy spectra. In non-Hermitian systems, distinctive spectral geometry can lead to topological braiding of complex-energy bands, yet directly probing this topology-geometry interplay remains challenging. Here, we introduce a Transformer-based ML framework to capture this interplay and experimentally demonstrate it in a dissipative cold-atom simulator. Using a Bose-Einstein condensate, we engineer tunable dissipative two-level systems whose complex eigenenergies form braids. Owing to the density-dependent dissipation, the instantaneous energy braids exhibit topologically distinct structures at short and long times. The Transformer not only accurately predicts topological invariants for diverse energy braids but also, through its self-attention mechanism, autonomously highlights band crossings as the governing underlying geometric feature. Our work paves the way for ML-guided exploration of non-Hermitian topological phases in cold atoms and beyond. Despite the increasing applications of machine learning in the quantum sciences, applications in the context of topological matter are still limited. Here, the authors demonstrate topological braiding of complex energy bands in a dissipative ultracold atom platform based on a transformer approach, advancing machine-learning-aided search of topological phases.

Source: Nature Communications

DOI: 10.1038/s41467-026-71880-4