Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Technical Review
  • Published:

Tools for quantum simulation with ultracold atoms in optical lattices

Nature Reviews Physics volume 2, pages 411–425 (2020)Cite this article

Subjects

Abstract

After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity at which it can be used to investigate complex quantum processes. Planning of new experiments and upgrading of existing set-ups requires a broad overview of the available techniques, their specific advantages and limitations. This Technical Review aims to provide a comprehensive compendium of the state of the art. We discuss the basic principles, the available techniques and their current range of applications. Focusing on the simulation of various phenomena in solid-state physics through optical lattice experiments, we review their basics, the necessary techniques and the accessible physical parameters. We outline how to control and use interactions with external potentials and interactions between the atoms, and how to design new synthetic gauge fields and spin–orbit coupling. We discuss the latest progress in site-resolved techniques that use quantum gas microscopes, and describe the unique features of quantum simulation experiments with two-electron atomic species.

Key points

  • Quantum simulation with ultracold atomic gases in optical lattices can be used to study condensed-matter quantum many-body systems, which are hard to simulate with conventional computers.

  • The control of interatomic interactions is key to successful quantum simulation, and it can be implemented at short range and long range through various methods.

  • Non-equilibrium phenomena can be studied by using controlled dissipation or lattice perturbations.

  • Quantum gas microscopes currently offer the most precise tool for the manipulation and readout of optical lattice quantum simulators.

  • The use of artificial gauge fields enables the simulation of charged particle physics; furthermore, non-trivial effects are accessible through use of spin–orbit coupling, topological lattices and synthetic dimensions.

  • Going from alkaline-earth-metal to two-electron alkaline-earth-metal-like atoms allows the study of SU(N) symmetrical systems.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Quantum simulation tools and applications.
Fig. 2: Optical lattice geometries and Bloch band structures.
Fig. 3: Controlling atomic interactions using magnetic, optical and confinement-induced Feshbach resonances.
Fig. 4: Controlled perturbations through disorder.
Fig. 5: Quantum gas microscope imaging and cooling methods.

Similar content being viewed by others

References

  1. Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

    ADS  Google Scholar 

  2. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

    Google Scholar 

  3. Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).

    ADS  Google Scholar 

  4. Greiner, M., Mandel, O., Esslinger, T., Hansch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).

    ADS  Google Scholar 

  5. Zohar, E., Cirac, J. I. & Reznik, B. Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices. Rep. Prog. Phys. 79, 014401 (2015).

    ADS  MathSciNet  Google Scholar 

  6. Giovanazzi, S. Hawking radiation in sonic black holes. Phys. Rev. Lett. 94, 061302 (2005).

    ADS  MathSciNet  Google Scholar 

  7. Randeria, M. & Taylor, E. Crossover from Bardeen–Cooper–Schrieffer to Bose–Einstein condensation and the unitary Fermi gas. Annu. Rev. Condens. Matter Phys. 5, 209–232 (2014).

    ADS  Google Scholar 

  8. Goldman, N., Budich, J. C. & Zoller, P. Topological quantum matter with ultracold gases in optical lattices. Nat. Phys. 12, 639–645 (2016).

    Google Scholar 

  9. Moriya, T. & Ueda, K. Antiferromagnetic spin fluctuation and superconductivity. Rep. Prog. Phys. 66, 1299–1341 (2003).

    ADS  Google Scholar 

  10. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).

    ADS  Google Scholar 

  11. Li, Z.-X. & Yao, H. Sign-problem-free fermionic quantum Monte Carlo: developments and applications. Annu. Rev. Condens. Matter Phys. 10, 337–356 (2019).

    ADS  Google Scholar 

  12. Tarruell, L. & Sanchez-Palencia, L. Quantum simulation of the Hubbard model with ultracold fermions in optical lattices. Comptes Rendus Phys. 19, 365–393 (2018).

    ADS  Google Scholar 

  13. Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998). Together with ref. 4, this landmark paper theoretically and experimentally establishes optical lattices as a fundamental tool for the study of quantum many-body systems by demonstrating how to use them in the experimental study of the Bose–Hubbard model.

    ADS  Google Scholar 

  14. Modugno, M., Ibañez-Azpiroz, J. & Pettini, G. Tight-binding models for ultracold atoms in optical lattices: general formulation and applications. Sci. China Phys. Mech. Astron. 59, 660001 (2016).

    Google Scholar 

  15. Duan, L.-M. M., Demler, E. & Lukin, M. D. Controlling spin exchange interactions of ultracold atoms in optical lattices. Phys. Rev. Lett. 91, 090402 (2003).

    ADS  Google Scholar 

  16. Micheli, A., Brennen, G. K. & Zoller, P. A toolbox for lattice-spin models with polar molecules. Nat. Phys. 2, 341–347 (2006).

    Google Scholar 

  17. Meinert, F. et al. Quantum quench in an atomic one-dimensional Ising chain. Phys. Rev. Lett. 111, 053003 (2013).

    ADS  Google Scholar 

  18. Simon, J. et al. Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307–312 (2011).

    ADS  Google Scholar 

  19. Orzel, C. Squeezed states in a Bose–Einstein condensate. Science 291, 2386–2389 (2001).

    ADS  Google Scholar 

  20. Greiner, M., Bloch, I., Mandel, O., Hänsch, T. W. & Esslinger, T. Exploring phase coherence in a 2D lattice of Bose–Einstein condensates. Phys. Rev. Lett. 87, 160405 (2001).

    ADS  Google Scholar 

  21. Wirth, G., Ölschläger, M. & Hemmerich, A. Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice. Nat. Phys. 7, 147–153 (2011).

    Google Scholar 

  22. Taie, S. et al. Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice. Sci. Adv. 1, e1500854 (2015).

    ADS  Google Scholar 

  23. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014). This study uses a honeycomb optical lattice to simulate the Haldane model and to explore its topological band structure, demonstrating the ability of the optical lattice quantum simulator to realize topological states of matter with what had been believed to be just toy models for theoretical studies.

    ADS  Google Scholar 

  24. Becker, C. et al. Ultracold quantum gases in triangular optical lattices. N. J. Phys. 12, 065025 (2010).

    Google Scholar 

  25. Jo, G.-B. et al. Ultracold atoms in a tunable optical kagome lattice. Phys. Rev. Lett. 108, 045305 (2012).

    ADS  Google Scholar 

  26. Struck, J. et al. Quantum simulation of frustrated classical magnetism in triangular optical lattices. Science 333, 996–999 (2011).

    ADS  Google Scholar 

  27. Mandel, O. et al. Coherent transport of neutral atoms in spin-dependent optical lattice potentials. Phys. Rev. Lett. 91, 010407 (2003).

    ADS  Google Scholar 

  28. Gadway, B., Pertot, D., Reimann, R. & Schneble, D. Superfluidity of interacting bosonic mixtures in optical lattices. Phys. Rev. Lett. 105, 045303 (2010).

    ADS  Google Scholar 

  29. Hara, H., Konishi, H., Nakajima, S., Takasu, Y. & Takahashi, Y. A three-dimensional optical lattice of ytterbium and lithium atomic gas mixture. J. Phys. Soc. Jpn 83, 014003 (2013).

    ADS  Google Scholar 

  30. Lamporesi, G. et al. Scattering in mixed dimensions with ultracold gases. Phys. Rev. Lett. 104, 153202 (2010).

    ADS  Google Scholar 

  31. Schäfer, F. et al. Experimental realization of ultracold Yb–7Li mixtures in mixed dimensions. Phys. Rev. A 98, 051602(R) (2018).

    ADS  Google Scholar 

  32. Konishi, H., Schäfer, F., Ueda, S. & Takahashi, Y. Collisional stability of localized Yb(3P 2) atoms immersed in a Fermi sea of Li. N. J. Phys. 18, 103009 (2016).

    Google Scholar 

  33. Viebahn, K., Sbroscia, M., Carter, E., Yu, J.-C. & Schneider, U. Matter-wave diffraction from a quasicrystalline optical lattice. Phys. Rev. Lett. 122, 110404 (2019).

    ADS  Google Scholar 

  34. Baumann, K., Guerlin, C., Brennecke, F. & Esslinger, T. Dicke quantum phase transition with a superfluid gas in an optical cavity. Nature 464, 1301–1306 (2010).

    ADS  Google Scholar 

  35. Fölling, S. et al. Direct observation of second-order atom tunnelling. Nature 448, 1029–1032 (2007).

    ADS  Google Scholar 

  36. Nakajima, S. et al. Topological Thouless pumping of ultracold fermions. Nat. Phys. 12, 296–300 (2016).

    Google Scholar 

  37. Lohse, M., Schweizer, C., Zilberberg, O., Aidelsburger, M. & Bloch, I. A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice. Nat. Phys. 12, 350–354 (2015).

    Google Scholar 

  38. Bergamini, S. et al. Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator. J. Opt. Soc. Am. B 21, 1889 (2004).

    ADS  MathSciNet  Google Scholar 

  39. Bakr, W. S., Gillen, J. I., Peng, A., Fölling, S. & Greiner, M. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74–77 (2009). Together with ref. 172, this study demonstrates how to combine optical lattices and high-resolution optical imaging to realize a quantum gas microscope, a tool that gives unprecedented single-site access to many-body systems.

    ADS  Google Scholar 

  40. Barredo, D., de Léséleuc, S., Lienhard, V., Lahaye, T. & Browaeys, A. An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays. Science 354, 1021–1023 (2016).

    ADS  Google Scholar 

  41. Bakr, W. S. et al. Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329, 547–550 (2010).

    ADS  Google Scholar 

  42. Fukuhara, T. et al. Quantum dynamics of a mobile spin impurity. Nat. Phys. 9, 235–241 (2013).

    Google Scholar 

  43. Endres, M. et al. Atom-by-atom assembly of defect-free one-dimensional cold atom arrays. Science 354, 1024–1027 (2016).

    ADS  Google Scholar 

  44. Barredo, D., Lienhard, V., Léséleuc, S., de, Lahaye, T. & Browaeys, A. Synthetic three-dimensional atomic structures assembled atom by atom. Nature 561, 79–82 (2018).

    ADS  Google Scholar 

  45. Kato, S. et al. Laser spectroscopic probing of coexisting superfluid and insulating states of an atomic Bose–Hubbard system. Nat. Commun. 7, 11341 (2016).

    ADS  Google Scholar 

  46. Nakamura, Y. et al. Experimental determination of Bose–Hubbard energies. Phys. Rev. A 99, 033609 (2019).

    ADS  Google Scholar 

  47. Campbell, S. L. et al. A Fermi-degenerate three-dimensional optical lattice clock. Science 358, 90–94 (2017).

    ADS  Google Scholar 

  48. Franchi, L. et al. State-dependent interactions in ultracold 174Yb probed by optical clock spectroscopy. N. J. Phys. 19, 103037 (2017).

    Google Scholar 

  49. Bouganne, R. et al. Clock spectroscopy of interacting bosons in deep optical lattices. N. J. Phys. 19, 113006 (2017).

    Google Scholar 

  50. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

    ADS  Google Scholar 

  51. Eckardt, A., Weiss, C. & Holthaus, M. Superfluid–insulator transition in a periodically driven optical lattice. Phys. Rev. Lett. 95, 260404 (2005).

    ADS  Google Scholar 

  52. Lignier, H. et al. Dynamical control of matter-wave tunneling in periodic potentials. Phys. Rev. Lett. 99, 220403 (2007).

    ADS  Google Scholar 

  53. Struck, J. et al. Tunable gauge potential for neutral and spinless particles in driven optical lattices. Phys. Rev. Lett. 108, 225304 (2012).

    ADS  Google Scholar 

  54. Jiménez-García, K. et al. Peierls substitution in an engineered lattice potential. Phys. Rev. Lett. 108, 225303 (2012).

    ADS  Google Scholar 

  55. Gaunt, A. L., Schmidutz, T. F., Gotlibovych, I., Smith, R. P. & Hadzibabic, Z. Bose–Einstein condensation of atoms in a uniform potential. Phys. Rev. Lett. 110, 200406 (2013).

    ADS  Google Scholar 

  56. Toth, E., Rey, A. M. & Blakie, P. B. Theory of correlations between ultracold bosons released from an optical lattice. Phys. Rev. A 78, 013627 (2008).

    ADS  Google Scholar 

  57. Köhl, M., Moritz, H., Stöferle, T., Günter, K. & Esslinger, T. Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions. Phys. Rev. Lett. 94, 080403 (2005).

    ADS  Google Scholar 

  58. Rey, A. M., Blakie, P. B., Pupillo, G., Williams, C. J. & Clark, C. W. Bragg spectroscopy of ultracold atoms loaded in an optical lattice. Phys. Rev. A 72, 023407 (2005).

    ADS  Google Scholar 

  59. Clément, D., Fabbri, N., Fallani, L., Fort, C. & Inguscio, M. Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering. Phys. Rev. Lett. 102, 155301 (2009).

    ADS  Google Scholar 

  60. Schori, C., Stöferle, T., Moritz, H., Köhl, M. & Esslinger, T. Excitations of a superfluid in a three-dimensional optical lattice. Phys. Rev. Lett. 93, 240402 (2004).

    ADS  Google Scholar 

  61. Stewart, J. T., Gaebler, J. P. & Jin, D. S. Using photoemission spectroscopy to probe a strongly interacting Fermi gas. Nature 454, 744–747 (2008).

    ADS  Google Scholar 

  62. Brown, P. T. et al. Angle-resolved photoemission spectroscopy of a Fermi–Hubbard system. Nat. Phys. 16, 26–31 (2020).

    Google Scholar 

  63. Dao, T.-L., Georges, A., Dalibard, J., Salomon, C. & Carusotto, I. Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy. Phys. Rev. Lett. 98, 240402 (2007).

    ADS  Google Scholar 

  64. Rom, T. et al. State selective production of molecules in optical lattices. Phys. Rev. Lett. 93, 073002 (2004).

    ADS  Google Scholar 

  65. Cocchi, E. et al. Equation of state of the two-dimensional Hubbard model. Phys. Rev. Lett. 116, 175301 (2016).

    ADS  Google Scholar 

  66. Campbell, G. K. et al. Imaging the Mott insulator shells by using atomic clock shifts. Science 313, 649–652 (2006).

    ADS  Google Scholar 

  67. Cennini, G., Ritt, G., Geckeler, C. & Weitz, M. All-optical realization of an atom laser. Phys. Rev. Lett. 91, 240408 (2003).

    ADS  Google Scholar 

  68. Taie, S. et al. Realization of a SU(2)×SU(6) system of fermions in a cold atomic gas. Phys. Rev. Lett. 105, 190401 (2010).

    ADS  Google Scholar 

  69. Trotzky, S., Chen, Y.-A., Schnorrberger, U., Cheinet, P. & Bloch, I. Controlling and detecting spin correlations of ultracold atoms in optical lattices. Phys. Rev. Lett. 105, 265303 (2010).

    ADS  Google Scholar 

  70. Ozawa, H., Taie, S., Takasu, Y. & Takahashi, Y. Antiferromagnetic spin correlation of SU(N) Fermi gas in an optical superlattice. Phys. Rev. Lett. 121, 225303 (2018).

    ADS  Google Scholar 

  71. Greif, D., Uehlinger, T., Jotzu, G., Tarruell, L. & Esslinger, T. Short-range quantum magnetism of ultracold fermions in an optical lattice. Science 340, 1307–1310 (2013).

    ADS  Google Scholar 

  72. Santra, B. et al. Measuring finite-range phase coherence in an optical lattice using Talbot interferometry. Nat. Commun. 8, 15601 (2017).

    ADS  Google Scholar 

  73. Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11, 162–166 (2015).

    Google Scholar 

  74. Asteria, L. et al. Measuring quantized circular dichroism in ultracold topological matter. Nat. Phys. 15, 449–454 (2019).

    Google Scholar 

  75. Mandel, O. et al. Controlled collisions for multi-particle entanglement of optically trapped atoms. Nature 425, 937–940 (2003).

    ADS  Google Scholar 

  76. Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225 (2010).

    ADS  Google Scholar 

  77. Enomoto, K., Kasa, K., Kitagawa, M. & Takahashi, Y. Optical Feshbach resonance using the intercombination transition. Phys. Rev. Lett. 101, 203201 (2008).

    ADS  Google Scholar 

  78. Blatt, S. et al. Measurement of optical Feshbach resonances in an ideal gas. Phys. Rev. Lett. 107, 073202 (2011).

    ADS  Google Scholar 

  79. Yan, M., DeSalvo, B. J., Ramachandhran, B., Pu, H. & Killian, T. C. Controlling condensate collapse and expansion with an optical Feshbach resonance. Phys. Rev. Lett. 110, 123201 (2013).

    ADS  Google Scholar 

  80. Thomas, O., Lippe, C., Eichert, T. & Ott, H. Experimental realization of a Rydberg optical Feshbach resonance in a quantum many-body system. Nat. Commun. 9, 2238 (2018).

    ADS  Google Scholar 

  81. Thalhammer, G., Theis, M., Winkler, K., Grimm, R. & Denschlag, J. H. Inducing an optical Feshbach resonance via stimulated Raman coupling. Phys. Rev. A 71, 033403 (2005).

    ADS  Google Scholar 

  82. Höfer, M. et al. Observation of an orbital interaction-induced Feshbach resonance in 173Yb. Phys. Rev. Lett. 115, 265302 (2015).

    ADS  Google Scholar 

  83. Pagano, G. et al. Strongly interacting gas of two-electron fermions at an orbital Feshbach resonance. Phys. Rev. Lett. 115, 265301 (2015).

    ADS  Google Scholar 

  84. Zhang, R., Cheng, Y., Zhai, H. & Zhang, P. Orbital Feshbach resonance in alkali-earth atoms. Phys. Rev. Lett. 115, 135301 (2015).

    ADS  Google Scholar 

  85. Bloch, I. Ultracold quantum gases in optical lattices. Nat. Phys. 1, 23–30 (2005).

    Google Scholar 

  86. Morsch, O. & Oberthaler, M. Dynamics of Bose–Einstein condensates in optical lattices. Rev. Mod. Phys. 78, 179–215 (2006).

    ADS  Google Scholar 

  87. Wang, Y. et al. Magnetic lattices for ultracold atoms and degenerate quantum gases. Sci. Bull. 61, 1097–1106 (2016).

    Google Scholar 

  88. Olshanii, M. Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Phys. Rev. Lett. 81, 938–941 (1998).

    ADS  Google Scholar 

  89. Moritz, H., Stöferle, T., Günter, K., Köhl, M. & Esslinger, T. Confinement induced molecules in a 1D Fermi gas. Phys. Rev. Lett. 94, 210401 (2005).

    ADS  Google Scholar 

  90. Haller, E. et al. Confinement-induced resonances in low-dimensional quantum systems. Phys. Rev. Lett. 104, 153203 (2010).

    ADS  Google Scholar 

  91. Bergeman, T., Moore, M. G. & Olshanii, M. Atom–atom scattering under cylindrical harmonic confinement: numerical and analytic studies of the confinement induced resonance. Phys. Rev. Lett. 91, 163201 (2003).

    ADS  Google Scholar 

  92. Griesmaier, A. Generation of a dipolar Bose–Einstein condensate. J. Phys. B At. Mol. Opt. 40, R91 (2007).

    ADS  Google Scholar 

  93. Lu, M., Burdick, N. Q., Youn, S. H. & Lev, B. L. Strongly dipolar Bose–Einstein condensate of dysprosium. Phys. Rev. Lett. 107, 190401 (2011).

    ADS  Google Scholar 

  94. Frisch, A. et al. Quantum chaos in ultracold collisions of gas-phase erbium atoms. Nature 507, 475–479 (2014).

    ADS  Google Scholar 

  95. Li, H., Wyart, J.-F., Dulieu, O. & Lepers, M. Anisotropic optical trapping as a manifestation of the complex electronic structure of ultracold lanthanide atoms: the example of holmium. Phys. Rev. A 95, 062508 (2017).

    ADS  Google Scholar 

  96. Griesmaier, A. et al. Comparing contact and dipolar interactions in a Bose–Einstein condensate. Phys. Rev. Lett. 97, 250402 (2006).

    ADS  Google Scholar 

  97. Gadway, B. & Yan, B. Strongly interacting ultracold polar molecules. J. Phys. B At. Mol. Opt. 49, 152002 (2016).

    ADS  Google Scholar 

  98. Moses, S. A., Covey, J. P., Miecnikowski, M. T., Jin, D. S. & Ye, J. New frontiers for quantum gases of polar molecules. Nat. Phys. 13, 13–20 (2017).

    Google Scholar 

  99. Ni, K.-K. et al. A high phase-space-density gas of polar molecules. Science 322, 231–235 (2008).

    ADS  Google Scholar 

  100. Will, S. A., Park, J. W., Yan, Z. Z., Loh, H. & Zwierlein, M. W. Coherent microwave control of ultracold 23Na 40K molecules. Phys. Rev. Lett. 116, 225306 (2016).

    ADS  Google Scholar 

  101. Guttridge, A. et al. Production of ultracold Cs* Yb molecules by photoassociation. Phys. Rev. A 97, 063414 (2018).

    ADS  Google Scholar 

  102. Zirbel, J. J. et al. Heteronuclear molecules in an optical dipole trap. Phys. Rev. A 78, 013416 (2008).

    ADS  Google Scholar 

  103. Shuman, E. S., Barry, J. F. & DeMille, D. Laser cooling of a diatomic molecule. Nature 467, 820–823 (2010).

    ADS  Google Scholar 

  104. Kozyryev, I. et al. Sisyphus laser cooling of a polyatomic molecule. Phys. Rev. Lett. 118, 173201 (2017).

    ADS  Google Scholar 

  105. Anderegg, L. et al. Laser cooling of optically trapped molecules. Nat. Phys. 14, 890–893 (2018).

    Google Scholar 

  106. Marco, L. D. et al. A degenerate Fermi gas of polar molecules. Science 363, 853–856 (2019).

    ADS  Google Scholar 

  107. Löw, R. et al. An experimental and theoretical guide to strongly interacting Rydberg gases. J. Phys. B 45, 113001 (2012).

    ADS  Google Scholar 

  108. Weimer, H., Müller, M., Lesanovsky, I., Zoller, P. & Büchler, H. P. A Rydberg quantum simulator. Nat. Phys. 6, 382–388 (2010).

    Google Scholar 

  109. Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010).

    ADS  Google Scholar 

  110. Léséleuc, Sde et al. Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms. Science 365, 775–780 (2019).

    ADS  MathSciNet  MATH  Google Scholar 

  111. Schauß, P. et al. Crystallization in Ising quantum magnets. Science 347, 1455–1458 (2015).

    ADS  Google Scholar 

  112. Guardado-Sanchez, E. et al. Probing the quench dynamics of antiferromagnetic correlations in a 2D quantum Ising spin system. Phys. Rev. X 8, 021069 (2018).

    Google Scholar 

  113. Lienhard, V. et al. Observing the space- and time-dependent growth of correlations in dynamically tuned synthetic Ising models with antiferromagnetic interactions. Phys. Rev. X 8, 021070 (2018).

    Google Scholar 

  114. Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).

    ADS  Google Scholar 

  115. Labuhn, H. et al. Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models. Nature 534, 667–670 (2016).

    ADS  Google Scholar 

  116. Urban, E. et al. Observation of Rydberg blockade between two atoms. Nat. Phys. 5, 110–114 (2009).

    Google Scholar 

  117. Gaëtan, A. et al. Observation of collective excitation of two individual atoms in the Rydberg blockade regime. Nat. Phys. 5, 115–118 (2009).

    Google Scholar 

  118. Zeiher, J. et al. Many-body interferometry of a Rydberg-dressed spin lattice. Nat. Phys. 12, 1095–1099 (2016).

    Google Scholar 

  119. de Léséleuc, S., Barredo, D., Lienhard, V., Browaeys, A. & Lahaye, T. Optical control of the resonant dipole–dipole interaction between Rydberg atoms. Phys. Rev. Lett. 119, 053202 (2017).

    ADS  Google Scholar 

  120. Anderson, S. E., Younge, K. C. & Raithel, G. Trapping Rydberg atoms in an optical lattice. Phys. Rev. Lett. 107, 263001 (2011).

    ADS  Google Scholar 

  121. Barredo, D. et al. Three-dimensional trapping of individual Rydberg atoms in ponderomotive bottle beam traps. Phys. Rev. Lett. 124, 023201 (2020).

    ADS  Google Scholar 

  122. Nguyen, T. L. et al. Towards quantum simulation with circular Rydberg atoms. Phys. Rev. X 8, 011032 (2018).

    Google Scholar 

  123. Hulet, R. G. & Kleppner, D. Rydberg atoms in ‘circular’ states. Phys. Rev. Lett. 51, 1430–1433 (1983).

    ADS  Google Scholar 

  124. Gaul, C. et al. Resonant Rydberg dressing of alkaline-earth atoms via electromagnetically induced transparency. Phys. Rev. Lett. 116, 243001 (2016).

    ADS  Google Scholar 

  125. Lüschen, H. P. et al. Signatures of many-body localization in a controlled open quantum system. Phys. Rev. X 7, 011034 (2017).

    Google Scholar 

  126. Labouvie, R., Santra, B., Heun, S., Wimberger, S. & Ott, H. Negative differential conductivity in an interacting quantum gas. Phys. Rev. Lett. 115, 050601 (2015).

    ADS  Google Scholar 

  127. Weiner, J., Bagnato, V. S., Zilio, S. & Julienne, P. S. Experiments and theory in cold and ultracold collisions. Rev. Mod. Phys. 71, 1–85 (1999).

    ADS  Google Scholar 

  128. Tomita, T., Nakajima, S., Danshita, I., Takasu, Y. & Takahashi, Y. Observation of the Mott insulator to superfluid crossover of a driven-dissipative Bose–Hubbard system. Sci. Adv. 3, e1701513 (2017).

    ADS  Google Scholar 

  129. Mark, M. J. et al. Preparation and spectroscopy of a metastable Mott-insulator state with attractive interactions. Phys. Rev. Lett. 108, 215302 (2012).

    ADS  Google Scholar 

  130. Daley, A. J. Quantum trajectories and open many-body quantum systems. Adv. Phys. 63, 77–149 (2014).

    ADS  Google Scholar 

  131. Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. Quantum Zeno effect. Phys. Rev. A 41, 2295–2300 (1990).

    ADS  Google Scholar 

  132. Syassen, N. et al. Strong dissipation inhibits losses and induces correlations in cold molecular gases. Science 320, 1329–1331 (2008). This work demonstrates how to use optical lattices and dissipation by inelastic collisions to reach the strongly correlated regime of many-body physics.

    ADS  Google Scholar 

  133. Schäfer, F. et al. Experimental realization of quantum Zeno dynamics. Nat. Commun. 5, 3194 (2014).

    ADS  Google Scholar 

  134. Signoles, A. et al. Confined quantum Zeno dynamics of a watched atomic arrow. Nat. Phys. 10, 715–719 (2014).

    Google Scholar 

  135. Pascazio, S. & Namiki, M. Dynamical quantum Zeno effect. Phys. Rev. A 50, 4582–4592 (1994).

    ADS  MathSciNet  Google Scholar 

  136. Viola, L. & Lloyd, S. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733–2744 (1998).

    ADS  MathSciNet  Google Scholar 

  137. Sponselee, K. et al. Dynamics of ultracold quantum gases in the dissipative Fermi–Hubbard model. Quantum Sci. Technol. 4, 014002 (2018).

    ADS  Google Scholar 

  138. Nakagawa, M., Tsuji, N., Kawakami, N. & Ueda, M. Dynamical sign reversal of magnetic correlations in dissipative Hubbard models. Phys. Rev. Lett. 124, 147203 (2020).

    ADS  Google Scholar 

  139. Bouganne, R., Aguilera, M. B., Ghermaoui, A., Beugnon, J. & Gerbier, F. Anomalous decay of coherence in a dissipative many-body system. Nat. Phys. 16, 1–5 (2019).

    Google Scholar 

  140. Pan, L., Chen, X., Chen, Y. & Zhai, H. Non-Hermitian linear response theory. Nat. Phys. https://doi.org/10.1038/s41567-020-0889-6 (2020).

    Article  Google Scholar 

  141. Ashida, Y., Furukawa, S. & Ueda, M. Parity-time-symmetric quantum critical phenomena. Nat. Commun. 8, 15791 (2017).

    ADS  Google Scholar 

  142. Billy, J. et al. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891–894 (2008).

    ADS  Google Scholar 

  143. Roati, G. et al. Anderson localization of a non-interacting Bose–Einstein condensate. Nature 453, 895–898 (2008). Ref. 142 and this paper demonstrate two different ways to introduce controlled disorder into optical lattices (using speckle patterns and incommensurable lattice wavelength, respectively) for the quantum simulation of disordered systems.

    ADS  Google Scholar 

  144. Günter, K., Stöferle, T., Moritz, H., Köhl, M. & Esslinger, T. Bose-fermi mixtures in a three-dimensional optical lattice. Phys. Rev. Lett. 96, 180402 (2006).

    ADS  Google Scholar 

  145. Ospelkaus, S. et al. Localization of bosonic atoms by fermionic impurities in a three-dimensional optical lattice. Phys. Rev. Lett. 96, 180403 (2006).

    ADS  Google Scholar 

  146. Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: Many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).

    ADS  MathSciNet  Google Scholar 

  147. Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).

    ADS  MathSciNet  MATH  Google Scholar 

  148. Langen, T., Geiger, R. & Schmiedmayer, J. Ultracold atoms out of equilibrium. Annu. Rev. Cond. Matter Phys. 6, 201–217 (2015).

    ADS  Google Scholar 

  149. Greiner, M., Mandel, O., Hänsch, T. W. & Bloch, I. Collapse and revival of the matter wave field of a Bose–Einstein condensate. Nature 419, 51–54 (2002).

    ADS  Google Scholar 

  150. Dziarmaga, J. & Rams, M. M. Dynamics of an inhomogeneous quantum phase transition. N. J. Phys. 12, 055007 (2010).

    Google Scholar 

  151. Chen, D., White, M., Borries, C. & DeMarco, B. Quantum quench of an atomic Mott insulator. Phys. Rev. Lett. 106, 235304 (2011).

    ADS  Google Scholar 

  152. Braun, S. et al. Emergence of coherence and the dynamics of quantum phase transitions. Proc. Natl Acad. Sci. USA 112, 3641–3646 (2015).

    ADS  Google Scholar 

  153. Cheneau, M. et al. Light-cone-like spreading of correlations in a quantum many-body system. Nature 481, 484–487 (2012).

    ADS  Google Scholar 

  154. Ronzheimer, J. P. et al. Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions. Phys. Rev. Lett. 110, 205301 (2013).

    ADS  Google Scholar 

  155. Schneider, U. et al. Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms. Nat. Phys. 8, 213–218 (2012).

    Google Scholar 

  156. Scherg, S. et al. Nonequilibrium mass transport in the 1D Fermi–Hubbard model. Phys. Rev. Lett. 121, 130402 (2018).

    ADS  Google Scholar 

  157. Xia, L. et al. Quantum distillation and confinement of vacancies in a doublon sea. Nat. Phys. 11, 316–320 (2015).

    Google Scholar 

  158. Hung, C.-L., Gurarie, V. & Chin, C. From cosmology to cold atoms: observation of Sakharov oscillations in a quenched atomic superfluid. Science 341, 1213–1215 (2013).

    ADS  Google Scholar 

  159. Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).

    ADS  Google Scholar 

  160. Gemelke, N., Zhang, X., Hung, C.-L. & Chin, C. In situ observation of incompressible Mott-insulating domains in ultracold atomic gases. Nature 460, 995–998 (2009).

    ADS  Google Scholar 

  161. Yamamoto, R. et al. Site-resolved imaging of single atoms with a Faraday quantum gas microscope. Phys. Rev. A 96, 033610 (2017).

    ADS  Google Scholar 

  162. Edge, G. J. A. et al. Imaging and addressing of individual fermionic atoms in an optical lattice. Phys. Rev. A 92, 063406 (2015).

    ADS  Google Scholar 

  163. Haller, E. et al. Single-atom imaging of fermions in a quantum-gas microscope. Nat. Phys. 11, 738–742 (2015).

    Google Scholar 

  164. Cheuk, L. W. et al. Quantum-gas microscope for fermionic atoms. Phys. Rev. Lett. 114, 193001 (2015).

    ADS  Google Scholar 

  165. Parsons, M. F. et al. Site-resolved imaging of fermionic 6Li in an optical lattice. Phys. Rev. Lett. 114, 213002 (2015).

    ADS  Google Scholar 

  166. Omran, A. et al. Microscopic observation of Pauli blocking in degenerate fermionic lattice gases. Phys. Rev. Lett. 115, 263001 (2015).

    ADS  Google Scholar 

  167. Yamamoto, R., Kobayashi, J., Kuno, T., Kato, K. & Takahashi, Y. An ytterbium quantum gas microscope with narrow-line laser cooling. N. J. Phys. 18, 023016 (2016).

    Google Scholar 

  168. Miranda, M., Inoue, R., Okuyama, Y., Nakamoto, A. & Kozuma, M. Site-resolved imaging of ytterbium atoms in a two-dimensional optical lattice. Phys. Rev. A 91, 063414 (2015).

    ADS  Google Scholar 

  169. Fukuhara, T. et al. Spatially resolved detection of a spin-entanglement wave in a Bose–Hubbard chain. Phys. Rev. Lett. 115, 035302 (2015).

    ADS  Google Scholar 

  170. Preiss, P. M., Ma, R., Tai, M. E., Simon, J. & Greiner, M. Quantum gas microscopy with spin, atom-number, and multilayer readout. Phys. Rev. A 91, 041602 (2015).

    ADS  Google Scholar 

  171. Boll, M. et al. Spin- and density-resolved microscopy of antiferromagnetic correlations in Fermi–Hubbard chains. Science 353, 1257–1260 (2016).

    ADS  MathSciNet  MATH  Google Scholar 

  172. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011).

    ADS  Google Scholar 

  173. Zupancic, P. et al. Ultra-precise holographic beam shaping for microscopic quantum control. Opt. Express 24, 13881–13893 (2016).

    ADS  Google Scholar 

  174. Cheuk, L. W. et al. Observation of 2D fermionic Mott insulators of 40K with single-site resolution. Phys. Rev. Lett. 116, 235301 (2016).

    ADS  Google Scholar 

  175. Greif, D. et al. Site-resolved imaging of a fermionic Mott insulator. Science 351, 953–957 (2016).

    ADS  MathSciNet  Google Scholar 

  176. Endres, M. et al. Observation of correlated particle–hole pairs and string order in low-dimensional Mott insulators. Science 334, 200–203 (2011).

    ADS  Google Scholar 

  177. Parsons, M. F. et al. Site-resolved measurement of the spin-correlation function in the Fermi–Hubbard model. Science 353, 1253–1256 (2016).

    ADS  MathSciNet  MATH  Google Scholar 

  178. Cheuk, L. W. et al. Observation of spatial charge and spin correlations in the 2D Fermi–Hubbard model. Science 353, 1260–1264 (2016).

    ADS  MathSciNet  MATH  Google Scholar 

  179. Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017).

    ADS  Google Scholar 

  180. Hilker, T. A. et al. Revealing hidden antiferromagnetic correlations in doped Hubbard chains via string correlators. Science 357, 484–487 (2017).

    ADS  MathSciNet  MATH  Google Scholar 

  181. Amico, L., Fazio, R., Osterloh, A. & Vedral, V. Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008).

    ADS  MathSciNet  MATH  Google Scholar 

  182. Islam, R. et al. Measuring entanglement entropy in a quantum many-body system. Nature 528, 77–83 (2015).

    ADS  Google Scholar 

  183. Preiss, P. M. et al. Strongly correlated quantum walks in optical lattices. Science 347, 1229–1233 (2015).

    ADS  MathSciNet  MATH  Google Scholar 

  184. Fukuhara, T. et al. Microscopic observation of magnon bound states and their dynamics. Nature 502, 76–79 (2013).

    ADS  Google Scholar 

  185. Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794–800 (2016).

    ADS  Google Scholar 

  186. Choi, J. et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016).

    ADS  MathSciNet  MATH  Google Scholar 

  187. Chiu, C. S., Ji, G., Mazurenko, A., Greif, D. & Greiner, M. Quantum state engineering of a Hubbard system with ultracold fermions. Phys. Rev. Lett. 120, 243201 (2018).

    ADS  Google Scholar 

  188. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    ADS  Google Scholar 

  189. Cooper, N. R., Dalibard, J. & Spielman, I. B. Topological bands for ultracold atoms. Rev. Mod. Phys. 91, 015005 (2019).

    ADS  MathSciNet  Google Scholar 

  190. Lin, Y.-J., Compton, R. L., Jiménez-García, K., Porto, J. V. & Spielman, I. B. Synthetic magnetic fields for ultracold neutral atoms. Nature 462, 628–632 (2009).

    ADS  Google Scholar 

  191. Aidelsburger, M. et al. Experimental realization of strong effective magnetic fields in an optical lattice. Phys. Rev. Lett. 107, 255301 (2011).

    ADS  Google Scholar 

  192. Miyake, H., Siviloglou, G. A., Kennedy, C. J., Burton, W. C. & Ketterle, W. Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices. Phys. Rev. Lett. 111, 185302 (2013).

    ADS  Google Scholar 

  193. Aidelsburger, M. et al. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301 (2013).

    ADS  Google Scholar 

  194. Kennedy, C. J., Burton, W. C., Chung, W. C. & Ketterle, W. Observation of Bose–Einstein condensation in a strong synthetic magnetic field. Nat. Phys. 11, 859–864 (2015).

    Google Scholar 

  195. Clark, L. W. et al. Observation of density-dependent gauge fields in a Bose–Einstein condensate based on micromotion control in a shaken two-dimensional lattice. Phys. Rev. Lett. 121, 030402 (2018).

    ADS  Google Scholar 

  196. Görg, F. et al. Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter. Nat. Phys. 15, 1161–1167 (2019).

    Google Scholar 

  197. Schweizer, C. et al. Floquet approach to Z2 lattice gauge theories with ultracold atoms in optical lattices. Nat. Phys. 15, 1168–1173 (2019).

    Google Scholar 

  198. Tarnowski, M. et al. Measuring topology from dynamics by obtaining the Chern number from a linking number. Nat. Commun. 10, 1728 (2019).

    ADS  Google Scholar 

  199. Stuhl, B. K., Lu, H.-I., Aycock, L. M., Genkina, D. & Spielman, I. B. Visualizing edge states with an atomic Bose gas in the quantum Hall regime. Science 349, 1514–1518 (2015).

    ADS  MathSciNet  MATH  Google Scholar 

  200. Mancini, M. et al. Observation of chiral edge states with neutral fermions in synthetic Hall ribbons. Science 349, 1510–1513 (2015). Together with ref. 199, this work uses an optical lattice to engineer synthetic dimensions and shows how to use this as a tool for the simulation of quantum Hall physics.

    ADS  MathSciNet  MATH  Google Scholar 

  201. Meier, E. J., An, F. A. & Gadway, B. Observation of the topological soliton state in the Su–Schrieffer–Heeger model. Nat. Commun. 7, 13986 (2016).

    ADS  Google Scholar 

  202. Celi, A. et al. Synthetic gauge fields in synthetic dimensions. Phys. Rev. Lett. 112, 043001 (2014).

    ADS  Google Scholar 

  203. Li, J. et al. Spin–orbit coupling and spin textures in optical superlattices. Phys. Rev. Lett. 117, 185301 (2016).

    ADS  Google Scholar 

  204. Li, J.-R. et al. A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).

    ADS  Google Scholar 

  205. Kolkowitz, S. et al. Spin–orbit-coupled fermions in an optical lattice clock. Nature 542, 66–70 (2017).

    ADS  Google Scholar 

  206. Livi, L. F. et al. Synthetic dimensions and spin–orbit coupling with an optical clock transition. Phys. Rev. Lett. 117, 220401 (2016).

    ADS  Google Scholar 

  207. Song, B. et al. Observation of nodal-line semimetal with ultracold fermions in an optical lattice. Nat. Phys. 15, 911–916 (2019).

    Google Scholar 

  208. Song, B. et al. Observation of symmetry-protected topological band with ultracold fermions. Sci. Adv. 4, eaao4748 (2018).

    ADS  Google Scholar 

  209. Wu, Z. et al. Realization of two-dimensional spin–orbit coupling for Bose–Einstein condensates. Science 354, 83–88 (2016).

    ADS  Google Scholar 

  210. Sun, W. et al. Highly controllable and robust 2D spin–orbit coupling for quantum gases. Phys. Rev. Lett. 121, 150401 (2018).

    ADS  Google Scholar 

  211. Sun, W. et al. Uncover topology by quantum quench dynamics. Phys. Rev. Lett. 121, 250403 (2018).

    ADS  Google Scholar 

  212. Cazalilla, M. A. & Rey, A. M. Ultracold Fermi gases with emergent SU(N) symmetry. Rep. Prog. Phys. 77, 124401 (2014).

    ADS  Google Scholar 

  213. Stellmer, S., Grimm, R. & Schreck, F. Detection and manipulation of nuclear spin states in fermionic strontium. Phys. Rev. A 84, 043611 (2011).

    ADS  Google Scholar 

  214. Richardson, R. C. The Pomeranchuk effect. Rev. Mod. Phys. 69, 683–690 (1997).

    ADS  Google Scholar 

  215. Taie, S., Yamazaki, R., Sugawa, S. & Takahashi, Y. An SU(6) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling. Nat. Phys. 8, 825–830 (2012). This work introduces the application of ultracold two-electron systems, here fermionic 173Yb, to the simulation of SU(N) many-body physics.

    Google Scholar 

  216. Hofrichter, C. et al. Direct probing of the Mott crossover in the SU(N) Fermi–Hubbard model. Phys. Rev. X 6, 021030 (2016).

    Google Scholar 

  217. Sleator, T., Pfau, T., Balykin, V., Carnal, O. & Mlynek, J. Experimental demonstration of the optical Stern–Gerlach effect. Phys. Rev. Lett. 68, 1996–1999 (1992).

    ADS  Google Scholar 

  218. Kato, S., Sugawa, S., Shibata, K., Yamamoto, R. & Takahashi, Y. Control of resonant interaction between electronic ground and excited states. Phys. Rev. Lett. 110, 173201 (2013).

    ADS  Google Scholar 

  219. Taie, S., Watanabe, S., Ichinose, T. & Takahashi, Y. Feshbach-resonance-enhanced coherent atom–molecule conversion with ultranarrow photoassociation resonance. Phys. Rev. Lett. 116, 043202 (2016).

    ADS  Google Scholar 

  220. Junker, M. et al. Photoassociation of a Bose–Einstein condensate near a feshbach resonance. Phys. Rev. Lett. 101, 060406 (2008).

    ADS  Google Scholar 

  221. Fedichev, P. O., Kagan, Yu., Shlyapnikov, G. V. & Walraven, J. T. M. Influence of nearly resonant light on the scattering length in low-temperature atomic gases. Phys. Rev. Lett. 77, 2913–2916 (1996).

    ADS  Google Scholar 

  222. Gorshkov, A. V. et al. Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms. Nat. Phys. 6, 289–295 (2010).

    Google Scholar 

  223. Cappellini, G. et al. Coherent manipulation of orbital Feshbach molecules of two-electron atoms. Phys. Rev. X 9, 011028 (2019).

    Google Scholar 

  224. Zhang, R. et al. Controlling the interaction of ultracold alkaline-earth atoms. Nat. Rev. Phys. 2, 213–220 (2020).

    Google Scholar 

  225. Foss-Feig, M., Hermele, M. & Rey, A. M. Probing the Kondo lattice model with alkaline-earth-metal atoms. Phys. Rev. A 81, 051603 (2010).

    ADS  Google Scholar 

  226. Cappellini, G. et al. Direct observation of coherent interorbital spin-exchange dynamics. Phys. Rev. Lett. 113, 120402 (2014).

    ADS  Google Scholar 

  227. Ono, K., Kobayashi, J., Amano, Y., Sato, K. & Takahashi, Y. Antiferromagnetic interorbital spin-exchange interaction of 171Yb. Phys. Rev. A 99, 032707 (2019).

    ADS  Google Scholar 

  228. Buluta, I. & Nori, F. Quantum simulators. Science 326, 108–111 (2009).

    ADS  Google Scholar 

  229. McKay, D. C. & DeMarco, B. Cooling in strongly correlated optical lattices: prospects and challenges. Rep. Prog. Phys. 74, 054401 (2011).

    ADS  Google Scholar 

  230. Kantian, A., Langer, S. & Daley, A. J. Dynamical disentangling and cooling of atoms in bilayer optical lattices. Phys. Rev. Lett. 120, 060401 (2018).

    ADS  Google Scholar 

  231. Goto, S. & Danshita, I. Cooling schemes for two-component fermions in layered optical lattices. Phys. Rev. A 96, 063602 (2017).

    ADS  Google Scholar 

  232. Kuroki, K., Kimura, T. & Arita, R. High-temperature superconductivity in dimer array systems. Phys. Rev. B 66, 184508 (2002).

    ADS  Google Scholar 

  233. Saffman, M. Quantum computing with atomic qubits and Rydberg interactions: progress and challenges. J. Phys. B 49, 202001 (2016).

    ADS  Google Scholar 

  234. Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).

    Google Scholar 

  235. Safronova, M. S. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018).

    ADS  MathSciNet  Google Scholar 

  236. Tarruell, L., Greif, D., Uehlinger, T., Jotzu, G. & Esslinger, T. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature 483, 302–305 (2012).

    ADS  Google Scholar 

  237. Guo, H., Zhu, X., Feng, S. & Scalettar, R. T. Pairing symmetry of interacting fermions on a twisted bilayer graphene superlattice. Phys. Rev. B 97, 235453 (2018).

    ADS  Google Scholar 

  238. Guo, H.-M. & Franz, M. Topological insulator on the kagome lattice. Phys. Rev. B 80, 113102 (2009).

    ADS  Google Scholar 

  239. Clément, D. et al. Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle. N. J. Phys. 8, 165–165 (2006).

    Google Scholar 

Download references

Acknowledgements

This work was supported through the Grants-in-Aid for Scientific Research (KAKENHI) programme of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) and the Japan Society for the Promotion of Science (JSPS) (grant nos 25220711, 17H06138, 18H05405, 18H05228 and 19H01854), the Impulsing Paradigm Change through Disruptive Technologies (ImPACT) programme, the CREST programme of the Japan Science and Technology (JST) Agency (grant no. JPMJCR1673), and the MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) (grant no. JPMXS0118069021). S.S. acknowledges support from the JST, PRESTO (grant no. JPMJPR1664) and JSPS (19K14639).

Author information

Authors and Affiliations

  1. Department of Physics, Graduate School of Science, Kyoto University, Kyoto, Japan

    Florian Schäfer, Yosuke Takasu & Yoshiro Takahashi

  2. RIKEN Center for Emergent Matter Science (CEMS), Saitama, Japan

    Takeshi Fukuhara

  3. Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, Japan

    Seiji Sugawa

  4. SOKENDAI (The Graduate University for Advanced Studies), Okazaki, Japan

    Seiji Sugawa

Authors
  1. Florian Schäfer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takeshi Fukuhara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seiji Sugawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yosuke Takasu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yoshiro Takahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors have read, discussed and contributed to the writing of the manuscript.

Corresponding author

Correspondence to Florian Schäfer.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Physics thanks Giovanni Modugno and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Schäfer, F., Fukuhara, T., Sugawa, S. et al. Tools for quantum simulation with ultracold atoms in optical lattices. Nat Rev Phys 2, 411–425 (2020). https://doi.org/10.1038/s42254-020-0195-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42254-020-0195-3

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing