Detecting Complex-Energy Braiding Topology in a Dissipative Atomic Simulator with Transformer-Based Geometric Tomography

TL;DR

This paper presents a Transformer-based machine learning framework that detects and analyzes complex-energy braiding topology in dissipative atomic systems, demonstrated experimentally with cold atoms.

Contribution

It introduces a novel Transformer-based approach to capture and interpret the interplay between topology and geometry in non-Hermitian quantum systems, validated experimentally.

Findings

Transformer accurately predicts topological invariants of energy braids.

Self-attention highlights band crossings as key geometric features.

Experimental demonstration with dissipative Bose-Einstein condensates.

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.