Quantum simulations with ultracold quantum gases

Journal name:
Nature Physics
Year published:
Published online


Ultracold quantum gases offer a unique setting for quantum simulation of interacting many-body systems. The high degree of controllability, the novel detection possibilities and the extreme physical parameter regimes that can be reached in these ‘artificial solids’ provide an exciting complementary set-up compared with natural condensed-matter systems, much in the spirit of Feynman’s vision of a quantum simulator. Here we review recent advances in technology and discuss progress in a number of areas where experimental results have already been obtained.

At a glance


  1. Equations of state of interacting ultracold Fermi gases.
    Figure 1: Equations of state of interacting ultracold Fermi gases.

    a, Schematic representation of the BEC–BCS crossover. For weak attractive interactions, atoms of opposite spin and momentum form Cooper pairs whose spatial extent greatly exceeds the mean interparticle distance. In the opposite limit of strongly attractive interactions, the gas is made of tightly bound molecules forming a BEC. In the middle of the crossover between the BCS and BEC regimes, the scattering length diverges at the unitary limit, leading to a strongly correlated state of matter. b, Equation of state of the ground state of a Fermi gas in the BEC–BCS crossover, expressed as the pressure normalized by the non-interacting pressure as a function of the interaction parameter . (For the definition of the Fermi momentum , see ref. 18.) The solid red line is obtained from the fixed-node diffusion Monte Carlo simulation of ref. 140 and the blue dots are experimental data from ref. 18. Panel reproduced with permission from ref. 18, © 2010 AAAS. c, Finite-temperature equation of state of the unitary Fermi gas. The dark (light) blue dots are the experimental data from ref. 40 (ref. 19) and the red dots are the bold diagrammatic Monte Carlo data from ref. 41. The grey area indicates the superfluid phase; the location of the normal/superfluid phase transition is taken from ref. 19. Panel reproduced with permission from ref. 19, © 2012 AAAS.

  2. Single-atom resolved images of a BEC and Mott insulators.
    Figure 2: Single-atom resolved images of a BEC and Mott insulators.

    a, A weakly interacting BEC. b,c, Strongly interacting Mott insulators in the atomic limit. The top row shows the raw-data fluorescence images. For higher atom numbers (c) a shell structure develops with a doubly occupied core in the centre. Owing to light-induced losses, the parity of the occupation number is detected in experiments (Box 2). The bottom row shows the results of an image-analysis algorithm through which the particle positions were reconstructed. Figure reproduced from ref. 80.

  3. Coherent control of single spins in an optical lattice.
    Figure 3: Coherent control of single spins in an optical lattice.

    a, By focussing an addressing laser onto single atoms, the energy splitting between two spin states can be controlled. A microwave source, resonant only with this shifted transition frequency, allows single-site-resolved spin control. b,c, By moving the addressing beam to different lattice sites, arbitrary spin patterns at the single-spin level can be prepared. Figure reproduced from ref. 88.

  4. Realization of a quantum Ising model using a one-dimensional Mott insulator in a strong potential gradient.
    Figure 4: Realization of a quantum Ising model using a one-dimensional Mott insulator in a strong potential gradient.

    When exposing a unit-filling Mott insulator to a potential gradient, neighbouring lattice sites are shifted in energy by Δ. For Δ<U, the Mott insulator corresponds to a paramagnetic phase (a), whereas for Δ>U an antiferromagnetic phase is formed as the ground state of the system (c). A transition between both states occurs around ΔU (b). The occupation of neighbouring sites represent pseudo-spins of the system (d). Lower row: direct single-site and single-atom resolved images of the transition from a paramagnetic to an antiferromagnetic phase. Panel reproduced from ref. 94.


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  1. Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4, 80799 München, Germany

    • Immanuel Bloch &
    • Sylvain Nascimbène
  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany

    • Immanuel Bloch
  3. Laboratoire Kastler Brossel, CNRS, UPMC, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France

    • Jean Dalibard &
    • Sylvain Nascimbène

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