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Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
Benno S. Rem, Niklas Käming, Matthias Tarnowski, Luca Asteria, Nick Fläschner, Christoph Becker, Klaus Sengstock, Christof Weitenberg
TL;DR
The paper addresses how to identify quantum phases from limited momentum-space images when conventional observables or complete state information are unavailable. It trains neural networks on experimental images and applies them to Haldane and Bose-Hubbard systems, showing phase-sensitive outputs and a new image-based route for analyzing transitions.
Problem
A Chern number is not obviously extractable from a single momentum-space image, motivating new analysis of limited experimental information.
Method
The approach learns phase information from experimental images far from transitions and classifies images across transition regions, alongside image-based PCA comparison.
Results
The network's superfluid-phase probability follows the modeled superfluid-fraction trend across the inhomogeneous Bose-Hubbard transition.
Takeaways & Limitations
Single-image neural-network analysis provides a new way to analyze quantum phase transitions and extract information unavailable from limited conventional state information.
Abstract
from arXiv · showhide
Machine learning techniques such as artificial neural networks are currently revolutionizing many technological areas and have also proven successful in quantum physics applications. Here we employ an artificial neural network and deep learning techniques to identify quantum phase transitions from single-shot experimental momentum-space density images of ultracold quantum gases and obtain results, which were not feasible with conventional methods. We map out the complete two-dimensional topological phase diagram of the Haldane model and provide an accurate characterization of the superfluid-to-Mott-insulator transition in an inhomogeneous Bose-Hubbard system. Our work points the way to unravel complex phase diagrams of general experimental systems, where the Hamiltonian and the order parameters might not be known.
Supplementary Material
The supplementary material details experimental preparation, inhomogeneous-system modeling, image-analysis comparisons, and robustness checks for the neural-network approach.
- Experimental setup: The Haldane experiment uses elliptical lattice forcing, with shaking phase and frequency controlling the Floquet system.Linear shaking preserves time-reversal symmetry, whereas circular shaking is used to produce the relevant Floquet properties.
- Bose-Hubbard modeling: The inhomogeneous Bose-Hubbard system is modeled with a local-density approximation, producing alternating superfluid and Mott-insulating shells.The calculated superfluid fraction decreases as successive Mott shells form, while small residual superfluid shells may become thermal experimentally.
- Image-analysis comparison: The simplified PCA compares images with averaged superfluid and Mott-insulator basis images through overlap coefficients that vary smoothly across the transition.The images are normalized and represented using basis-image coefficients obtained by solving a linear system.
- Robustness checks: Haldane-image classification accuracy begins dropping at about 50 pixels, approximately half a reciprocal-lattice-vector length.The result comes from cropping images to different diameters and repeating network training five times.
- Robustness checks: Bose-Hubbard transition identification remains insensitive to cropping down to around 30 pixels, much smaller than the reciprocal-lattice-vector length.This indicates that the network does not rely on visibility for identifying the phase transition.
- Robustness checks: The network assigns opposite Chern-number signs after vertical or combined horizontal-and-vertical image flipping.The supplementary evaluation compares unflipped, horizontally flipped, vertically flipped, and doubly flipped images.