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arXiv:1904.08074 · Measurement Science and Technology

Deep learning-assisted classification of site-resolved quantum gas microscope images

Lewis R. B. Picard, Manfred J. Mark, Francesca Ferlaino, Rick van Bijnen

Published Sep 18, 2019• 22 citations
arXivHTMLPDF

Abstract

Abstract We present a novel method for the analysis of quantum gas microscope images, which uses deep learning to improve the fidelity with which lattice sites can be classified as occupied or unoccupied. Our method is especially suited to addressing the case of imaging without continuous cooling, in which the accuracy of existing threshold-based reconstruction methods is limited by atom motion and low photon counts. We devise two neural network architectures which are both able to improve upon the fidelity of threshold-based methods, following training on large data sets of simulated images. We evaluate these methods on simulations of a free-space erbium quantum gas microscope, and a noncooled ytterbium microscope in which atoms are pinned in a deep lattice during imaging. In some conditions we see reductions of up to a factor of two in the reconstruction error rate, representing a significant step forward in our efforts to implement high fidelity noncooled site-resolved imaging.

DOI
10.1088/1361-6501/ab44d8

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•Jun 1, 2017•0 citations
Abstract We present a novel method for the analysis of quantum gas microscope images, which uses deep learning to improve the fidelity with which lattice sites can be classified as occupied or unoccupied. Our method is especially suited to addressing the case of imaging without continuous cooling, in which the accuracy of existing threshold-based reconstruction methods is limited by atom motion and low photon counts. We devise two neural network architectures which are both able to improve upon the fidelity of threshold-based methods, following training on large data sets of simulated images. We evaluate these methods on simulations of a free-space erbium quantum gas microscope, and a noncooled ytterbium microscope in which atoms are pinned in a deep lattice during imaging. In some conditions we see reductions of up to a factor of two in the reconstruction error rate, representing a significant step forward in our efforts to implement high fidelity noncooled site-resolved imaging.
Abstract In quantum gas microscopy experiments, reconstructing the site-resolved lattice occupation with high fidelity is essential for the accurate extraction of physical observables. For short interatomic separations and limited signal-to-noise ratio, this task becomes increasingly challenging. Common methods rapidly decline in performance as the lattice spacing is decreased below half the imaging resolution. Here, we present an algorithm based on deep convolutional neural networks to reconstruct the site-resolved lattice occupation with high fidelity. The algorithm can be directly trained in an unsupervised fashion with experimental fluorescence images and allows for a fast reconstruction of large images containing several thousand lattice sites. We benchmark its performance using a quantum gas microscope with cesium atoms that utilizes short-spaced optical lattices with lattice constant 383.5 nm and a typical Rayleigh resolution of 850 nm. We obtain promising reconstruction fidelities ≳ 96% across all fillings based on a statistical analysis. We anticipate this algorithm to enable novel experiments with shorter lattice spacing, boost the readout fidelity and speed of lower-resolution imaging systems, and furthermore find application in related experiments such as trapped ions.
Abstract The site-resolved detection of ultracold atoms in optical lattice potentials is a powerful technique to study lattice models of correlated quantum matter. In their recent paper, Yamamoto et al (2016 New J. Phys. 18 023016 ) demonstrate a quantum gas microscope for ultracold ytterbium atoms. By simultaneously cooling these atoms on two optical transitions, they show that fluorescent images of the lattice gas can be obtained while keeping the atoms pinned to their lattice sites even for a lattice spacing as small as 266 nm. This promises to be a powerful enabling tool for studies of metrology and quantum magnetism with quantum degenerate gases of ytterbium.
Quantum correlation, as an intrinsic property of quantum mechanics, has been widely employed to test the fundamental physical principles and explore the quantum-enhanced technologies. However, such correlation would be drowned and even destroyed in the conditions of high levels of loss and noise, which drops into the classical realm and renders quantum advantage ineffective. Especially in low light conditions, conventional linear classifiers are unable to extract and distinguish quantum and classical correlations with high accuracy. Here we experimentally demonstrate the classification of quantum correlation using deep learning to meet the challenge in the quantum imaging scheme. We design the convolutional neural network to learn and classify the correlated photons efficiently with only 0.1 signal photons per pixel. We show that decreasing signal intensity further weakens the correlation and makes an accurate linear classification impossible, while the deep learning method has a strong robustness of such task with the accuracy of 99.99%. These results open up a new perspective to optimize the quantum correlation in low light conditions, representing a step towards diverse applications in quantum-enhanced measurement scenarios, such as super-resolution microscope, quantum illumination, etc.
We apply deep-neural-network-based techniques to quantum state classification and reconstruction. Our methods demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feed-forward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed QST technique with conditional generative adversarial networks (QST-CGAN) [Ahmed et al., Phys. Rev. Lett. 127, 140502 (2021)]. We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than iterative and accelerated projected-gradient-based maximum-likelihood estimation (MLE) methods. We also demonstrate that the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than these MLE methods. Our paper opens possibilities to use state-of-the-art deep-learning methods for quantum state classification and reconstruction under various types of noise.
Abstract Quantum-gas microscopes are used to study ultracold atoms in optical lattices at the single-particle level. In these systems atoms are localised on lattice sites with separations close to or below the diffraction limit. To determine the lattice occupation with high fidelity, a deconvolution of the images is often required. We compare three different techniques, a local iterative deconvolution algorithm, Wiener deconvolution and the Lucy–Richardson algorithm, using simulated microscope images. We investigate how the reconstruction fidelity scales with varying signal-to-noise ratio, lattice filling fraction, varying fluorescence levels per atom, and imaging resolution. The results of this study identify the limits of singe-atom detection and provide quantitative fidelities which are applicable for different atomic species and quantum-gas microscope setups.
This thesis describes the methods used to achieve single-atom and single-site resolved fluorescence imaging of a quantum gas of fermionic atoms held in an optical lattice. This kind of quantum gas microscopy has been previously applied to bosonic atoms in two experiments, and has allowed for extensive studies of many-body quantum systems. Here we detail methods to extend the techniques of quantum gas microscopy to fermionic species of atoms, opening the door to quantum simulation of electronic models of condensed matter physics. We prepare quantum degenerate gases of fermionic 40K through sympathetic cooling with a gas of \Rb. The gas prepared is trapped less than 1 mm away from a thin vacuum window, an experimental geometry which permits interrogation with a large Numerical Aperture microscope objective. The cloud is loaded into a 527 nm-period cubic optical lattice, ideal for quantum simulation of many-body models of fermionic particles such as the Hubbard model. The optical lattice is designed to allow for potential depths up to V/kB = 250 microKelvin, sufficient to strongly confine 40K atoms into individual lattice sites. EIT cooling --- a technique previously demonstrated in ion-trapping experiments --- is used to cool the fermionic atoms deeply towards the ground motional state of the lattice wells. We collect the photons scattered during continuous application of EIT cooling, while atoms are kept pinned in the lattice for many seconds. We strongly suppress all other sources of light with the use of a modulated cooling scheme and a spinning chopper wheel. Collecting the scattered light produced during 2 s of EIT cooling allows us to resolve single atoms in a fluorescence image. We demonstrate that the high resolution of our imaging apparatus also permits atom positions to be precisely identified on the length scale of the optical lattice. Thus we demonstrate the realisation of a quantum gas microscope for fermionic atoms, allowing for precise investigation of the ground states and dynamics of correlated quantum states of fermionic particles.