Single-atom-resolved fluorescence imaging of an atomic Mott insulator

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The reliable detection of single quantum particles has revolutionized the field of quantum optics and quantum information processing. For several years, researchers have aspired to extend such detection possibilities to larger-scale, strongly correlated quantum systems1, 2 in order to record in situ images of a quantum fluid in which each underlying quantum particle is detected. Here we report fluorescence imaging of strongly interacting bosonic Mott insulators in an optical lattice with single-atom and single-site resolution. From our images, we fully reconstruct the atom distribution on the lattice and identify individual excitations with high fidelity. A comparison of the radial density and variance distributions with theory provides a precise in situ temperature and entropy measurement from single images. We observe Mott-insulating plateaus with near-zero entropy and clearly resolve the high-entropy rings separating them, even though their width is of the order of just a single lattice site. Furthermore, we show how a Mott insulator melts with increasing temperature, owing to a proliferation of local defects. The ability to resolve individual lattice sites directly opens up new avenues for the manipulation, analysis and applications of strongly interacting quantum gases on a lattice. For example, one could introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes3.

At a glance


  1. Experimental set-up.
    Figure 1: Experimental set-up.

    Two-dimensional bosonic quantum gases are prepared in a single two-dimensional plane of an optical standing wave along the z direction, which is created by retroreflecting a laser beam (λ = 1,064nm) on the coated vacuum window. Additional lattice beams along the x and y directions are used to bring the system into the strongly correlated regime of a Mott insulator. The atoms are detected using fluorescence imaging via a high-resolution microscope objective. Fluorescence of the atoms was induced by illuminating the quantum gas with an optical molasses that simultaneously laser-cools the atoms. The inset shows a section from a fluorescence picture of a dilute thermal cloud (points mark the lattice sites).

  2. High-resolution fluorescence images of a BEC and Mott insulators.
    Figure 2: High-resolution fluorescence images of a BEC and Mott insulators.

    The top row shows experimentally obtained raw images of a BEC (a) and Mott insulators for increasing particle numbers (bg) in the zero-tunnelling limit. The middle row shows numerically reconstructed atom distribution on the lattice. The images were convoluted with the point spread function (* indicates the convolution operator) of our imaging system for comparison with the original images. The bottom row shows the reconstructed atom number distribution. Each circle indicates a single atom; the points mark the lattice sites. The BEC and Mott insulators were prepared with the same in-plane harmonic confinement (see Supplementary Information for the Bose–Hubbard model parameters of our system).

  3. Identification of single atoms in a high-resolution image.
    Figure 3: Identification of single atoms in a high-resolution image.

    The points mark the centres of the lattice sites; circles indicate those sites where our deconvolution algorithm determined the presence of an atom. The image is a zoom into the upper right part of Fig. 2g.

  4. Radial atom density and variance profiles.
    Figure 4: Radial atom density and variance profiles.

    Radial profiles were obtained from the digitally reconstructed images by azimuthal averaging. a, b, Yellow and red points correspond to the n = 1 and n = 2 Mott insulator images of Fig. 2d and e. The grey points were obtained from a BEC (data from Fig. 2a) for reference. The displayed statistical error bars are Clopper–Pearson 68% confidence intervals for the binomially distributed number of excitations. For the Mott insulators, both average density and variance profiles are fitted simultaneously with the model functions of equations (1) and (2) (see Methods) with T, µ and as free parameters. For the two curves, the fits yielded temperatures T = 0.090(5)U/kB and T = 0.074(5)U/kB, chemical potentials µ = 0.73(3)U and µ = 1.17(1)U, and radii r0 = 5.7(1)µm and r0 = 5.95(4)µm, respectively. From the fitted values of T, µ and r0, we determined the atom numbers of the system to N = 270(20) and N = 529(8). c, d, The same data plotted versus the local chemical potential using the local-density approximation. The inset of c is a Bose–Hubbard phase diagram (T = 0) showing the transition between the characteristic Mott insulator lobes (grey shading) and the superfluid region. The straight line with arrow shows the part of the phase diagram existing simultaneously at different radii in the trap owing to the external harmonic confinement. The inset of d shows the entropy density calculated for the displayed n = 2 Mott insulator.

  5. Melting of a Mott insulator.
    Figure 5: Melting of a Mott insulator.

    ac, Strongly correlated atomic samples for three different temperatures and constant total chemical potential in the zero-tunnelling limit. For higher temperatures, an increased number of independent particles or holes appear. The data shown was binned 2×2. d, e, Density and variance profiles as a function of chemical potential, determined as described in the caption of Fig. 4. Red, orange and yellow points correspond to the data sets from a, b and c, respectively. Grey points correspond to the low-temperature n = 2 Mott insulator of Fig. 2e and Fig. 4 with T = 0.074(5)U/kB and µ = 1.17(1)U. The parameters extracted from the radial fits are T = 0.17(1)U/kB, µ = 2.08(4)U/kB for a, T = 0.20(2)U/kB, µ = 2.10(5)U/kB for b and T = 0.25(2)U/kB, µ = 2.06(7)U/kB for c.


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Author information

  1. These authors contributed equally to this work.

    • Jacob F. Sherson &
    • Christof Weitenberg


  1. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany

    • Jacob F. Sherson,
    • Christof Weitenberg,
    • Manuel Endres,
    • Marc Cheneau,
    • Immanuel Bloch &
    • Stefan Kuhr
  2. Ludwig-Maximilians-Universität, Schellingstraße 4/II, D-80799 München, Germany

    • Immanuel Bloch
  3. Present address: Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark.

    • Jacob F. Sherson


All authors contributed to the construction of the apparatus, acquisition and analysis of the data, and the writing of this manuscript.

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The authors declare no competing financial interests.

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  1. Supplementary Information (163K)

    This file contains Supplementary Notes 1-3 and Supplementary Figures 1-2 with legends.

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