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.Ultracold quantum gases have established as a formidable experimental platform to study paradigmatic quantum many-body systems in a well-controlled environment (1, 2). Important break-throughs include the realization of paradigmatic condensed matter models such as the Mott insulator transition or topological quantum matter. While these systems offer complementary observables to solid state systems, finding proper observables for quantum phases remains a key challenge, in particular in exotic systems such as non-local topological order of many-body localization. Here we explore a new approach building on modern machine learning techniques (3). Inspired by the success of convolutional neural networks in image recognition, we feed such networks with single images of momentum-space density, which are a standard experimental output of quantum gas experiments. We train it on large data sets of labelled images taken far away from the phase transition and apply the trained network to test data across the phase transition. The network is able to identify the correct position of the phase transition in parameter space from single experimental images. This is crucial advance for optimizing parameters, because the phase can now be determined from single images for direct decisions in the laboratory, and points towards future fully automated quantum simulators. We expect these techniques to be valuable also for in-situ snapshots as captured by quantum gas microscopes (4, 5). Similar approaches were previously applied to numerical Monte Carlo simulations of various physical models (6)(7)(8)(9)(10)(11)(12)(13). Neural networks are also opening new avenues in other areas of quantum physics, such as the representation of quantum many-body states (14,15) or the optimization of complex systems (16)(17)(18).We demonstrate the power of artificial neural networks on two physical examples, namely the topological phase transition in the Haldane model and the superfluid-to-Mott-insulator transition in the Bose-Hubbard model, both realized for cold atoms in optical lattices. We show that we can perform tasks, which were not possible with conventional techniques, such as the determination of non-local topological order from a sing...

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.