Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2012.13097 · Machine Learning Science and Technology

Deep-learning-based quantum vortex detection in atomic Bose–Einstein condensates

Friederike Metz, Juan Polo, Natalya Weber, Thomas Busch

Published Feb 26, 2021• 23 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2632-2153/abea6a

Related papers

Vortex detection in atomic Bose–Einstein condensates using neural networks trained on synthetic images

Myeonghyeon Kim, Junhwan Kwon, Tenzin Rabga +1 more

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.

arXiv:2308.08405•Machine Learning Science and Technology•Oct 16, 2023•8 citations

U-net based vortex detection in Bose–Einstein condensates with automatic correction for manually mislabeled data

Jing Ye, Yue Huang, Keyan Liu

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.

Scientific Reports•Dec 2, 2023•1 citation

CNN-Based vortex detection in atomic 2D Bose gases in the presence of a phononic background

Magnus Sesodia, Shinichi Sunami, En Chang +3 more

Abstract Quantum vortices play a crucial role in both equilibrium and dynamical phenomena in two-dimensional (2D) superfluid systems. Experimental detection of these excitations in 2D ultracold atomic gases typically involves examining density depletions in absorption images, however the presence of a significant phononic background renders the problem challenging, beyond the capability of simple algorithms or the human eye. Here, we utilize a convolutional neural network to detect vortices in the presence of strong long- and intermediate-length scale density modulations in finite-temperature 2D Bose gases. We train the model on datasets obtained from ab initio Monte Carlo simulations using the classical-field method for density and phase fluctuations, and Gross–Pitaevskii simulation of realistic expansion dynamics. We use the model to analyze experimental images and benchmark its performance by comparing the results to the matter-wave interferometric detection of vortices, confirming the observed scaling of vortex density across the Berezinskii–Kosterlitz–Thouless critical point. The combination of a relevant simulation pipeline with machine-learning methods is a key development towards the comprehensive understanding of complex vortex-phonon dynamics in out-of-equilibrium 2D quantum systems.

arXiv:2410.13829•Machine Learning Science and Technology•Mar 12, 2025•1 citation

Machine Learning Phase Field Reconstruction in a Bose-Einstein Condensate

Jackson Lee, Andrew J. Millis

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.

arXiv:2604.09528•Apr 10, 2026•0 citations

Chaotic Vortex Dynamics in Bose-Einstein Condensates

Tiantian Zhang

Quantum vortices in superfluid Bose Einstein condensates (BECs) are excellent candidates\nfor studying hydrodynamic phenomena, such as turbulence and chaos, due to the\nquantization of vortex circulation and the absence of dissipation in BECs. Since the early\n2000s, many experimental groups have successfully observed vortices in dilute atomic\nBECs.\n\nThis work mainly focuses on creating quantum chaos with a few vortices in a twodimensional\nBEC of Rubidium􀀀87. We use graphics processing unit (GPU) computing methods to simulate our BEC trapped inside a harmonic potential with tight trapping in one direction. The quantum vortices are created by rotating the condensate. After generating the ground state of the BEC with a small number of singly charged vortices with positive phase winding, we imprint a 4\\pi phase winding on top of one vortex in the opposite orientation to that of the original vortex. This phase imprinting annihilates the preexisting vortex and creates a new singly-charged vortex with negative phase winding. Due to the high resolution of our system and an excellent vortex tracking algorithm, the location of phase imprinting can be delicately controlled.\n\nBoth the individual vortex dynamics and the dynamics of the entire system of vortices\nafter flipping a vortex have shown strong signs of chaos. This chaotic nature is\nfurther confirmed both qualitatively and quantitatively by employing two chaos indicators\non our numerical results. These chaos indicators are the Lyapunov exponent spectrum\nand the Smaller ALignment Index (SALI). The Lyapunov exponent remains positive and\nconverges to a positive value during an experimentally realistic time period, which is the\nsmoking gun for chaotic behaviour.

•Jan 1, 2017•2 citations

Methods of Generation and Detection of Vorticity in Atomic Bose-Einstein Condensates

Samuel Nerenberg

Dilute gas Bose-Einstein condensates (BECs) provide unique and powerful experimental platforms to study fluid turbulence. Some aspects of BEC hydrodynamics are specific to atomic quantum fluids such as quantized vortices and flexible trapping geometries. However, there are features of turbulence that are universal and simpler to understand in such systems. BECs are also of interest in fundamental physics in their own right and a rich synthesis of theory and experiment has yielded powerful numerical methods to simulate and study BEC dynamics. In this dissertation I present two experiments, one conducted and one proposed, describing novel aspects of the generation and detection of vorticity in Bose-Einstein condensates. Models of BEC dynamics at zero temperature are provided by the Gross-Pitaevskii equation. Simple and fast numerical solutions of this equation have yielded a wealth of literature. However, in experimental reality the atomic ensemble exists at a finite temperature and consists of a BEC coexisting with a thermal cloud of non-condensed atoms. The interaction between the condensate and the thermal fraction yields rich and complex physics that require more advanced models. We present an experiment demonstrating the relaxation dynamics of a BEC in a rotating trap perturbed by a repulsive laser barrier. The data provided by this experiment are valuable to further development of theoretical models that incorporate interactions between the BEC and noncondensed atoms. In the field of quantum fluid dynamics, an experimental method to determine the position and circulation of vortices is a highly sought-after capability. Onsager's point-vortex model of turbulence completely determines the kinetic energy spectrum of an incompressible fluid by these degrees of freedom. We present proof-of-principle simulations that describe a new method of spatially sampling the velocity field of a two-dimensional BEC by using an optical lattice analogously to a Shack-Hartmann Wavefront Sensor. Extracting vortex information from the appropriately sampled velocity field can be accomplished either qualitatively or with detection algorithms. This method requires minimal experimental infrastructure and is generally applicable across atomic species. The implications of measuring a condensate velocity field are broad and these initial results provide the first step towards realizing a valuable tool in BEC physics.

•Jan 1, 2020•0 citations
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.
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.
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 play a crucial role in both equilibrium and dynamical phenomena in two-dimensional (2D) superfluid systems. Experimental detection of these excitations in 2D ultracold atomic gases typically involves examining density depletions in absorption images, however the presence of a significant phononic background renders the problem challenging, beyond the capability of simple algorithms or the human eye. Here, we utilize a convolutional neural network to detect vortices in the presence of strong long- and intermediate-length scale density modulations in finite-temperature 2D Bose gases. We train the model on datasets obtained from ab initio Monte Carlo simulations using the classical-field method for density and phase fluctuations, and Gross–Pitaevskii simulation of realistic expansion dynamics. We use the model to analyze experimental images and benchmark its performance by comparing the results to the matter-wave interferometric detection of vortices, confirming the observed scaling of vortex density across the Berezinskii–Kosterlitz–Thouless critical point. The combination of a relevant simulation pipeline with machine-learning methods is a key development towards the comprehensive understanding of complex vortex-phonon dynamics in out-of-equilibrium 2D quantum systems.
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 superfluid Bose Einstein condensates (BECs) are excellent candidates\nfor studying hydrodynamic phenomena, such as turbulence and chaos, due to the\nquantization of vortex circulation and the absence of dissipation in BECs. Since the early\n2000s, many experimental groups have successfully observed vortices in dilute atomic\nBECs.\n\nThis work mainly focuses on creating quantum chaos with a few vortices in a twodimensional\nBEC of Rubidium􀀀87. We use graphics processing unit (GPU) computing methods to simulate our BEC trapped inside a harmonic potential with tight trapping in one direction. The quantum vortices are created by rotating the condensate. After generating the ground state of the BEC with a small number of singly charged vortices with positive phase winding, we imprint a 4\\pi phase winding on top of one vortex in the opposite orientation to that of the original vortex. This phase imprinting annihilates the preexisting vortex and creates a new singly-charged vortex with negative phase winding. Due to the high resolution of our system and an excellent vortex tracking algorithm, the location of phase imprinting can be delicately controlled.\n\nBoth the individual vortex dynamics and the dynamics of the entire system of vortices\nafter flipping a vortex have shown strong signs of chaos. This chaotic nature is\nfurther confirmed both qualitatively and quantitatively by employing two chaos indicators\non our numerical results. These chaos indicators are the Lyapunov exponent spectrum\nand the Smaller ALignment Index (SALI). The Lyapunov exponent remains positive and\nconverges to a positive value during an experimentally realistic time period, which is the\nsmoking gun for chaotic behaviour.
Dilute gas Bose-Einstein condensates (BECs) provide unique and powerful experimental platforms to study fluid turbulence. Some aspects of BEC hydrodynamics are specific to atomic quantum fluids such as quantized vortices and flexible trapping geometries. However, there are features of turbulence that are universal and simpler to understand in such systems. BECs are also of interest in fundamental physics in their own right and a rich synthesis of theory and experiment has yielded powerful numerical methods to simulate and study BEC dynamics. In this dissertation I present two experiments, one conducted and one proposed, describing novel aspects of the generation and detection of vorticity in Bose-Einstein condensates. Models of BEC dynamics at zero temperature are provided by the Gross-Pitaevskii equation. Simple and fast numerical solutions of this equation have yielded a wealth of literature. However, in experimental reality the atomic ensemble exists at a finite temperature and consists of a BEC coexisting with a thermal cloud of non-condensed atoms. The interaction between the condensate and the thermal fraction yields rich and complex physics that require more advanced models. We present an experiment demonstrating the relaxation dynamics of a BEC in a rotating trap perturbed by a repulsive laser barrier. The data provided by this experiment are valuable to further development of theoretical models that incorporate interactions between the BEC and noncondensed atoms. In the field of quantum fluid dynamics, an experimental method to determine the position and circulation of vortices is a highly sought-after capability. Onsager's point-vortex model of turbulence completely determines the kinetic energy spectrum of an incompressible fluid by these degrees of freedom. We present proof-of-principle simulations that describe a new method of spatially sampling the velocity field of a two-dimensional BEC by using an optical lattice analogously to a Shack-Hartmann Wavefront Sensor. Extracting vortex information from the appropriately sampled velocity field can be accomplished either qualitatively or with detection algorithms. This method requires minimal experimental infrastructure and is generally applicable across atomic species. The implications of measuring a condensate velocity field are broad and these initial results provide the first step towards realizing a valuable tool in BEC physics.