Dimitris G Angelakis | Searcharxiv

arXiv2022

Dark soliton detection using persistent homology

Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers, but require extensive data and computational resources to train. We show how a topological data analysis technique, persistent homology, can be used to rapidly and reliably identify qualitative features in experimental image data. The identified features can be used as inputs to simple supervised machine learning models such as logistic regression models, which are easier to train. As an example we consider the identification of dark solitons using a dataset of 6257 labelled atomic Bose-Einstein condensate density images.

physics.atom-ph↗

arXiv2021

Photonic band structure design using persistent homology

The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to characterize physical systems such as spin models and multiqubit entangled states. Here we propose persistent homology as a tool for characterizing and optimizing band structures of periodic photonic media. Using the honeycomb photonic lattice Haldane model as an example, we show how persistent homology is able to reliably classify a variety of band structures falling outside the usual paradigms of topological band theory, including "moat band" and multi-valley dispersion relations, and thereby control the properties of quantum emitters embedded in the lattice. The method is promising for the automated design of more complex systems such as photonic crystals and Moire superlattices.

physics.optics↗