Abstract
Optical lattice experiments with ultracold atoms allow for the experimental realization of contemporary problems in many-body physics. Yet, devising models that faithfully describe experimental observables is often difficult and problem dependent; there is currently no theoretical method which accounts for all experimental observations. Leveraging the large data volume and presence of strong correlations, machine learning provides a novel avenue for the study of such systems. It has recently been proven successful in analyzing properties of experimental data of ultracold quantum gases. Here we show that generative deep learning succeeds in the challenging task of modeling such an experimental data distribution. Our method is able to produce synthetic experimental snapshots of a doped two-dimensional Fermi-Hubbard model that are indistinguishable from previously reported experimental realizations. We demonstrate how our generative model interprets physical conditions such as temperature at the level of individual configurations. We use our approach to predict snapshots at conditions and scales which are currently experimentally inaccessible, mapping the large-scale behavior of optical lattices at unseen conditions.
Highlights
Ultracold atoms provide a controlled environment for the study of emergent phenomena in many-body physical systems—including high-temperature superconductivity, many-body localization, and topological quantum phases— and have applications in fields such as cosmology and quantum chemistry [1,2,3,4]
The output of regressive upscaling generative adversarial network” (RUGAN) is a series of synthetic snapshots at prescribed doping values [Fig. 2(a)]
Alternate unsupervised machine learning methods, such as dimensionality reduction, are not capable of discriminating between the experimental samples and those created by RUGAN [see Fig. 2(b)]
Summary
Ultracold atoms provide a controlled environment for the study of emergent phenomena in many-body physical systems—including high-temperature superconductivity, many-body localization, and topological quantum phases— and have applications in fields such as cosmology and quantum chemistry [1,2,3,4]. The capability of discriminative machine learning to analyze physical systems has been well established, both for data obtained through numerical simulations [5,6,7,8,9,10,11,12], and for experimental observations through electronic quantum matter visualization [13], quantum gas microscopy [14,15], or momentum-space density images [16]. We show that our generative model is able to generalize in two ways: (i) it can create microstates with properties for which no training data is available, and (ii) it is able to create samples at a much larger scale (or “upscale”) than the training examples The former is relevant for systems where obtaining configurations is only numerically or experimentally feasible for a limited set of system properties. Appendix D describes the theoretical frameworks to which we compare our results
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