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arXiv:2209.10060 · Optics Express

Observing a topological phase transition with deep neural networks from experimental images of ultracold atoms

Entong Zhao, Ting Hin Mak, Chengdong He, Zejian Ren, Ka Kwan Pak, Yu-Jun Liu, Gyu-Boong Jo

Published Sep 21, 2022• 8 citations
arXivHTMLPDF

Abstract

Although classifying topological quantum phases have attracted great interests, the absence of local order parameter generically makes it challenging to detect a topological phase transition from experimental data. Recent advances in machine learning algorithms enable physicists to analyze experimental data with unprecedented high sensitivities, and identify quantum phases even in the presence of unavoidable noises. Here, we report a successful identification of topological phase transitions using a deep convolutional neural network trained with low signal-to-noise-ratio (SNR) experimental data obtained in a symmetry-protected topological system of spin-orbit-coupled fermions. We apply the trained network to unseen data to map out a whole phase diagram, which predicts the positions of the two topological phase transitions that are consistent with the results obtained by using the conventional method on higher SNR data. By visualizing the filters and post-convolutional results of the convolutional layer, we further find that the CNN uses the same information to make the classification in the system as the conventional analysis, namely spin imbalance, but with an advantage concerning SNR. Our work highlights the potential of machine learning techniques to be used in various quantum systems.

DOI
10.1364/oe.473770

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Machine Learning (ML) techniques have emerged as a powerful tool in quantum matter research. In this poster, we highlight how ML algorithms enable us to analyze experimental data with unprecedented high sensitivities and identify topological phases even in the presence of unavoidable noises. To this end, we apply the trained network to low signal-to-noise-ratio (SNR) experimental data obtained in a symmetry-protected topological system of spin-orbit-coupled fermions [1]. The obtained phase diagram by ML is consistent with the results obtained by using the conventional method on higher SNR data. Our work highlights the potential of machine learning techniques to be used in various quantum systems.
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Abstract Topologically ordered materials may serve as a platform for new quantum technologies, such as fault-tolerant quantum computers. To fulfil this promise, efficient and general methods are needed to discover and classify new topological phases of matter. We demonstrate that deep neural networks augmented with external memory can use the density profiles formed in quantum walks to efficiently identify properties of a topological phase as well as phase transitions. On a trial topological ordered model, our method’s accuracy of topological phase identification reaches 97.4%, and is shown to be robust to noise on the data. Furthermore, we demonstrate that our trained DNN is able to identify topological phases of a perturbed model, and predict the corresponding shift of topological phase transitions without learning any information about the perturbations in advance. These results demonstrate that our approach is generally applicable and may be used to identify a variety of quantum topological materials.
Abstract Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries from noisy and imperfect data without the knowledge of the order parameter. Here, we apply different unsupervised machine learning techniques, including anomaly detection and influence functions, to experimental data from ultracold atoms. In this way, we obtain the topological phase diagram of the Haldane model in a completely unbiased fashion. We show that these methods can successfully be applied to experimental data at finite temperatures and to the data of Floquet systems when post-processing the data to a single micromotion phase. Our work provides a benchmark for the unsupervised detection of new exotic phases in complex many-body systems.
The identification of phases of matter is a challenging task, especially in quantum mechanics, where the complexity of the ground state appears to grow exponentially with the size of the system. Traditionally, physicists have to identify the relevant order parameters for the classification of the different phases. We here follow a radically different approach: we address this problem with a state-of-the-art deep learning technique, adversarial domain adaptation. We derive the phase diagram of the whole parameter space starting from a fixed and known subspace using unsupervised learning. This method has the advantage that the input of the algorithm can be directly the ground state without any ad hoc feature engineering. Furthermore, the dimension of the parameter space is unrestricted. More specifically, the input data set contains both labeled and unlabeled data instances. The first kind is a system that admits an accurate analytical or numerical solution, and one can recover its phase diagram. The second type is the physical system with an unknown phase diagram. Adversarial domain adaptation uses both types of data to create invariant feature extracting layers in a deep learning architecture. Once these layers are trained, we can attach an unsupervised learner to the network to find phase transitions. We show the success of this technique by applying it on several paradigmatic models: the Ising model with different temperatures, the Bose-Hubbard model, and the Su-Schrieffer-Heeger model with disorder. The method finds unknown transitions successfully and predicts transition points in close agreement with standard methods. This study opens the door to the classification of physical systems where the phase boundaries are complex such as the many-body localization problem or the Bose glass phase.
Abstract We propose a systematic methodology to identify the topological phase transition through a self-supervised machine learning model, which is trained to correlate system parameters to the non-local observables in time-of-flight experiments of ultracold atoms. Different from the conventional supervised learning approach, where the predicted phase transition point is very sensitive to the training region and data labeling, our self-supervised learning approach identifies the phase transition point by the largest deviation of the predicted results from the known system parameters and by the highest confidence through a systematic shift of the training regions. We demonstrate the robust application of this approach results in various 1D and 2D exactly solvable models, using different input features (time-of-flight images, spatial correlation function or density–density correlation function). As a result, our self-supervised approach should be a very general and reliable method for many condensed matter or solid state systems to observe new states of matters solely based on experimental measurements, even without a priori knowledge of the phase transition models.