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arXiv:1710.08392 · Physical Review A

Single-atom-resolved probing of lattice gases in momentum space

Hugo Cayla, Cécile Carcy, Quentin Bouton, R. Chang, Giuseppe Carleo, M. Mancini, David Clément

Published Jun 26, 2018• 31 citations
arXivHTMLPDF

Abstract

Measuring the full distribution of individual particles is of fundamental importance to characterize many-body quantum systems through correlation functions at any order. Here, we demonstrate the possibility to reconstruct the momentum-space distribution of three-dimensional interacting lattice gases atom by atom. This is achieved by detecting individual metastable $^{4}\mathrm{He}^{*}$ atoms in the far-field regime of expansion, when released from an optical lattice. We benchmark our technique with quantum Monte Carlo calculations, demonstrating the ability to resolve momentum distributions of superfluids occupying ${10}^{5}$ lattice sites. It permits a direct measure of the condensed fraction across phase transitions, as we illustrate on the superfluid-to-normal transition. Our single-atom-resolved approach opens a route to investigate interacting lattice gases through momentum correlations.

DOI
10.1103/physreva.97.061609

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Measuring the full distribution of individual particles is of fundamental importance to characterize many-body quantum systems through correlation functions at any order. Here, we demonstrate the possibility to reconstruct the momentum-space distribution of three-dimensional interacting lattice gases atom by atom. This is achieved by detecting individual metastable 4He∗^{4}\mathrm{He}^{*}4He∗ atoms in the far-field regime of expansion, when released from an optical lattice. We benchmark our technique with quantum Monte Carlo calculations, demonstrating the ability to resolve momentum distributions of superfluids occupying 105{10}^{5}105 lattice sites. It permits a direct measure of the condensed fraction across phase transitions, as we illustrate on the superfluid-to-normal transition. Our single-atom-resolved approach opens a route to investigate interacting lattice gases through momentum correlations.
Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We used single atom-single lattice site imaging to investigate the Bose-Hubbard model on a microscopic level. Our technique enables space- and time-resolved characterization of the number statistics across the superfluid-Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low-entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition time scales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low-entropy phases in a lattice.
Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments, whereas in cold gases systems, time-of-flight, and in situ absorption imaging are the standard observation techniques. However, none of these methods allow the in situ detection of spatially resolved correlation functions at the single-particle level. Here, we give a more detailed account of recent advances in the detection of correlation functions using in situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site- and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
Quantum gas microscopy provides single-shot access to many-body configurations, yet has so far relied on pinning atoms to a discrete lattice during fluorescence readout. Here, we realize ultrafast atom-resolved fluorescence microscopy of an ultracold 162^{162}162Dy gas directly in free space, with all external confinement removed during imaging. Exploiting the large mass and broad optical transition of dysprosium together with a high numerical aperture in-vacuum objective, we detect single atoms within 4 μs4\,μ\mathrm{s}4μs while maintaining an effective point-spread function with a full width at half maximum of 254.8(3) nm254.8(3)\,\mathrm{nm}254.8(3)nm. We achieve a single-atom conditional classification fidelity of 99.72(3)%99.72(3)\%99.72(3)% for identified fluorescence candidates. We use the measured single-atom response to construct a statistical configuration-inference model that recovers atomic positions and multiplicities, coming from overlapping atoms, directly from single fluorescence snapshots. We further benchmark our reconstruction algorithm through end-to-end Monte Carlo simulations with known ground-truth atomic configurations, obtaining a reconstruction fidelity of 98.7%98.7\%98.7%. Our approach, applicable to a wide variety of atomic species, extends quantum gas microscopy beyond predefined detection lattices, enabling atom-resolved measurements of counting statistics and higher-order spatial correlations directly on the intrinsic length scales of continuum many-body systems.
This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice. We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism. In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing scheme leaves most atoms in the vibrational ground state. Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available. The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.