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arXiv:2111.01981 · Physical Review A

Machine-learning classification of two-dimensional vortex configurations

Rama Shankar Sharma, Tapio Simula

Published Mar 1, 2022• 4 citations
arXivHTMLPDF

Abstract

We consider computer-generated configurations of quantized vortices in planar superfluid Bose-Einstein condensates. We show that unsupervised machine-learning technology can successfully be used for classifying such vortex configurations to identify prominent vortex phases of matter. The machine-learning approach could thus be applied for automatically classifying large data sets of vortex configurations obtainable by experiments on two-dimensional quantum turbulence.

DOI
10.1103/physreva.105.033301

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We consider computer-generated configurations of quantized vortices in planar superfluid Bose-Einstein condensates. We show that unsupervised machine-learning technology can successfully be used for classifying such vortex configurations to identify prominent vortex phases of matter. The machine-learning approach could thus be applied for automatically classifying large data sets of vortex configurations obtainable by experiments on two-dimensional quantum turbulence.
Abstract Quantum vortices naturally emerge in rotating Bose–Einstein condensates (BECs) and, similarly to their classical counterparts, allow the study of a range of interesting out-of-equilibrium phenomena, such as turbulence and chaos. However, the study of such phenomena requires the determination of the precise location of each vortex within a BEC, which becomes challenging when either only the density of the condensate is available or sources of noise are present, as is typically the case in experimental settings. Here, we introduce a machine-learning-based vortex detector motivated by state-of-the-art object detection methods that can accurately locate vortices in simulated BEC density images. Our model allows for robust and real-time detection in noisy and non-equilibrium configurations. Furthermore, the network can distinguish between vortices and anti-vortices if the phase profile of the condensate is also available. We anticipate that our vortex detector will be advantageous for both experimental and theoretical studies of the static and dynamic properties of vortex configurations in BECs.
A basic challenge in experimental physics is the extraction of information related to variables that are not directly measured. The challenge is particularly severe in quantum systems where one may be interested in correlations of operators that are not diagonal in the measurement basis. In this paper we take a step towards addressing this issue in the context of Boson superfluids, where standard in-situ imaging yields only the spatially resolved density, leaving the phase field - crucial for identifying topological defects such as vortices and confirming superfluidity - indirectly encoded. Previous work has shown that the location of vortices in the phase field may be detected, but has not solved the problems of fully reconstructing the phase or identifying the charge (vortex vs. antivortex). This paper shows that a combination of a deep machine learning (ML) model and classical computer vision post-processing steps can address this gap. We use realistic snapshots of the thermal state of a two-dimensional BEC in a harmonic trap using synthetic data obtained from projected Gross-Pitaevskii equation simulations to train a U-Net-based architecture to infer the absolute values of the phase field gradients from an observed density field, and then employ a separate ML model to locate the positions of the vortex cores and a post-processing graphical analysis to determine with high accuracy the phase field, including the quantized charge of each vortex.
Quantum vortices in Bose-Einstein condensates (BECs) are essential phenomena in condensed matter physics, and precisely locating their positions, especially the vortex core, is a precondition for studying their properties. With the rise of machine learning, there is a possibility to expedite the localization process and provide accurate predictions. However, traditional machine learning requires particular considerable amount of manual data annotation, leading to uncontrollable accuracy. In this paper, we utilize the U-Net method to detect vortex positions accurately at the pixel level and propose an Automatic Correction Labeling (ACL) approach to optimize the acquisition of data sets for vortex localization in BECs. This approach addresses inaccuracies in the labeled vortex positions and improves the accuracy of vortex localization, especially the vortex core positions, while enhancing the tolerance for human mislabeling. The main process involves Rough Labeling [Formula: see text] Machine Learning [Formula: see text] Probability Region Search [Formula: see text] Data Relabeling [Formula: see text] Machine Learning again. The objective of ACL is to secure more accurate labeled data for model retraining. Through vortex localization experiments conducted in a two-dimensional Bose-Einstein condensate, our results establish the following: 1. Even under conditions of biased and missing manual annotations, U-Net can still accurately locate vortex positions; 2. Vortices exhibit certain regularities, and training U-Net with a small number of samples yields excellent predictive consequences; 3. The machine learning vortex locator based on the ACL method effectively corrects errors in manually annotated data, significantly improving the model's performance metrics, thus enhancing the precision and metrics of vortex localization. This substantial advancement in the application of machine learning in vortex localization provides an effective way for vortex dynamics localization. Furthermore, this method of obtaining more accurate positions of approximate human labels through machine learning offers new insights for machine learning in other types of image recognition problems.
Abstract Quantum vortices in atomic Bose–Einstein condensates (BECs) are topological defects characterized by quantized circulation of particles around them. In experimental studies, vortices are commonly detected by time-of-flight imaging, where their density-depleted cores are enlarged. In this work, we describe a machine learning-based method for detecting vortices in experimental BEC images, particularly focusing on turbulent condensates containing irregularly distributed vortices. Our approach employs a convolutional neural network (CNN) trained solely on synthetic simulated images, eliminating the need for manual labeling of the vortex positions as ground truth. We find that the CNN achieves accurate vortex detection in real experimental images, thereby facilitating analysis of large experimental datasets without being constrained by specific experimental conditions. This novel approach represents a significant advancement in studying quantum vortex dynamics and streamlines the analysis process in the investigation of turbulent BECs.
Bose-Einstein condensates of dilute gases are well-suited for investigations of vortex dynamics and turbulence in quantum fluids, yet there has been little experimental research into the approaches that may be most promising for generating states of two-dimensional turbulence in these systems. Here we give an overview of techniques for generating the large and disordered vortex distributions associated with two-dimensional quantum turbulence. We focus on describing methods explored in our Bose-Einstein condensation laboratory, and discuss the suitability of these methods for studying various aspects of two-dimensional quantum turbulence. We also summarize some of the open questions regarding our own understanding of these mechanisms of two-dimensional quantum turbulence generation in condensates. We find that while these disordered distributions of vortices can be generated by a variety of techniques, further investigation is needed to identify methods for obtaining quasi-steady-state quantum turbulence in condensates.
Unsupervised learning is a discipline of machine learning which aims at discovering patterns in large data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many-body systems. Starting with raw spin configurations of a prototypical Ising model, we use principal component analysis to extract relevant low-dimensional representations of the original data and use clustering analysis to identify distinct phases in the feature space. This approach successfully finds physical concepts such as the order parameter and structure factor to be indicators of a phase transition. We discuss the future prospects of discovering more complex phases and phase transitions using unsupervised learning techniques.