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

Area of Science:

• Quantum physics
• Condensed matter physics
• Machine learning applications

Background:

• Topological matter is defined by quantum state or energy spectrum geometry.
• Non-Hermitian systems exhibit unique spectral geometry leading to topological band braiding.
• Directly probing the interplay between topology and geometry in these systems is difficult.

Purpose of the Study:

• To introduce a Transformer-based machine learning framework to capture the topology-geometry interplay in non-Hermitian systems.
• To experimentally demonstrate this framework in a dissipative cold-atom simulator.
• To explore the potential of machine learning for discovering novel topological phases.

Main Methods:

• Utilizing a Bose-Einstein condensate to engineer tunable dissipative two-level systems.
• Creating complex eigenenergy braids with density-dependent dissipation.
• Employing a Transformer-based machine learning model to analyze energy braids and predict topological invariants.

Main Results:

• The Transformer model accurately predicts topological invariants for various energy braids.
• The self-attention mechanism of the Transformer autonomously identifies band crossings as key geometric features.
• Experimentally observed distinct topological structures in energy braids at short and long times due to dissipation.

Conclusions:

• The developed machine learning framework effectively captures the topology-geometry interplay in non-Hermitian systems.
• The study demonstrates a novel approach for experimental realization and analysis of topological phenomena in cold atoms.
• This work opens avenues for machine learning-guided exploration of non-Hermitian topological phases.