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Quantum simulations with ultracold quantum gases

Nature Physics volume 8, pages 267–276 (2012)Cite this article

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Abstract

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.

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Figure 1: Equations of state of interacting ultracold Fermi gases.
Figure 2: Single-atom resolved images of a BEC and Mott insulators.
Figure 3: Coherent control of single spins in an optical lattice.
Figure 4: Realization of a quantum Ising model using a one-dimensional Mott insulator in a strong potential gradient.

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References

  1. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

    Article  MathSciNet  Google Scholar 

  2. Inguscio, M., Ketterle, W. & Salomon, C. Ultra-cold Fermi Gases: Proceedings of the International School of Physics ‘Enrico Fermi’, course clxiv, Varenna (2008).

  3. Randeria, M., Zwerger, W. & Zwierlein, M. (eds) in The BCS–BEC Crossover and the Unitary Fermi Gas Vol. 836 (Lecture Notes in Physics, Springer, 2012).

  4. Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215–1274 (2008).

    Article  ADS  Google Scholar 

  5. Bardeen, J., Cooper, L. & Schrieffer, J. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  6. Petrov, D., Salomon, C. & Shlyapnikov, G. Weakly bound dimers of fermionic atoms. Phys. Rev. Lett. 93, 090404 (2004).

    Article  ADS  Google Scholar 

  7. Werner, F. & Castin, Y. Unitary quantum three-body problem in a harmonic trap. Phys. Rev. Lett. 97, 150401 (2006).

    Article  ADS  Google Scholar 

  8. Tan, S. Large momentum part of a strongly correlated Fermi gas. Ann. Phys. 323, 2971–2986 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Ho, T. Universal thermodynamics of degenerate quantum gases in the unitarity limit. Phys. Rev. Lett. 92, 090402 (2004).

    Article  ADS  Google Scholar 

  10. Bertsch, G. in Proceedings of the Tenth International Conference on Recent Progress in Many-Body Theories (eds Bishop, R., Gernoth, K. A., Walet, N. R. & Xian, Y.) (World Scientific, 2000).

    Google Scholar 

  11. O’Hara, K., Hemmer, S., Gehm, M., Granade, S. & Thomas, J. Observation of a strongly interacting degenerate Fermi gas of atoms. Science 298, 2179–2182 (2002).

    Article  ADS  Google Scholar 

  12. Bourdel, T. et al. Experimental study of the BEC–BCS crossover region in lithium 6. Phys. Rev. Lett. 93, 050401 (2004).

    Article  ADS  Google Scholar 

  13. Stewart, J., Gaebler, J., Regal, C. & Jin, D. Potential energy of a 40K Fermi gas in the BCS–BEC crossover. Phys. Rev. Lett. 97, 220406 (2006).

    Article  ADS  Google Scholar 

  14. Bartenstein, M. et al. Crossover from a molecular Bose–Einstein condensate to a degenerate Fermi gas. Phys. Rev. Lett. 92, 120401 (2004).

    Article  ADS  Google Scholar 

  15. Partridge, G., Li, W., Kamar, R., Liao, Y. & Hulet, R. Pairing and phase separation in a polarized Fermi gas. Science 311, 503–505 (2006).

    Article  ADS  Google Scholar 

  16. Joseph, J. et al. Measurement of sound velocity in a Fermi gas near a Feshbach resonance. Phys. Rev. Lett. 98, 170401 (2007).

    Article  ADS  Google Scholar 

  17. Kinast, J. et al. Heat capacity of a strongly interacting Fermi gas. Science 307, 1296–1299 (2005).

    Article  ADS  Google Scholar 

  18. Navon, N., Nascimbène, S., Chevy, F. & Salomon, C. The equation of state of a low-temperature Fermi gas with tunable interactions. Science 328, 729–732 (2010).

    Article  ADS  Google Scholar 

  19. Ku, M. J. H., Sommer, A. T., Cheuk, L. W. & Zwierlein, M. W. Revealing the superfluid Lambda transition in the universal thermodynamics of a unitary Fermi gas. Science 335, 563–567 (2012).

    Article  ADS  Google Scholar 

  20. Carlson, J., Chang, S., Pandharipande, V. & Schmidt, K. Superfluid Fermi gases with large scattering length. Phys. Rev. Lett. 91, 050401 (2003).

    Article  ADS  Google Scholar 

  21. Astrakharchik, G., Boronat, J., Casulleras, J. & Giorgini, S. Equation of state of a Fermi gas in the BEC–BCS crossover: A quantum Monte Carlo study. Phys. Rev. Lett. 93, 200404 (2004).

    Article  ADS  MATH  Google Scholar 

  22. Altmeyer, A. et al. Precision measurements of collective oscillations in the BEC–BCS crossover. Phys. Rev. Lett. 98, 040401 (2007).

    Article  ADS  Google Scholar 

  23. Astrakharchik, G. E., Combescot, R., Leyronas, X. & Stringari, S. Equation of state and collective frequencies of a trapped Fermi gas along the BEC–unitarity crossover. Phys. Rev. Lett. 95, 030404 (2005).

    Article  ADS  Google Scholar 

  24. Nascimbène, S. et al. Fermi-liquid behavior of the normal phase of a strongly interacting gas of cold atoms. Phys. Rev. Lett. 106, 215303 (2011).

    Article  ADS  Google Scholar 

  25. Sommer, A., Ku, M., Roati, G. & Zwierlein, M. Universal spin transport in a strongly interacting Fermi gas. Nature 472, 201–204 (2011).

    Article  ADS  Google Scholar 

  26. Zwierlein, M., Schirotzek, A., Schunck, C. & Ketterle, W. Fermionic superfluidity with imbalanced spin populations. Science 311, 492–496 (2006).

    Article  ADS  Google Scholar 

  27. Shin, Y., Schunck, C., Schirotzek, A. & Ketterle, W. Phase diagram of a two-component Fermi gas with resonant interactions. Nature 451, 689–693 (2008).

    Article  ADS  Google Scholar 

  28. Shin, Y. Determination of the equation of state of a polarized Fermi gas at unitarity. Phys. Rev. A 77, 041603 (2008).

    Article  ADS  Google Scholar 

  29. Schirotzek, A., Wu, C., Sommer, A. & Zwierlein, M. Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms. Phys. Rev. Lett. 102, 230402 (2009).

    Article  ADS  Google Scholar 

  30. Nascimbene, S. et al. Collective oscillations of an imbalanced Fermi gas: Axial compression modes and polaron effective mass. Phys. Rev. Lett. 103, 170402 (2009).

    Article  ADS  Google Scholar 

  31. Haussmann, R. Properties of a Fermi liquid at the superfluid transition in the crossover region between BCS superconductivity and Bose–Einstein condensation. Phys. Rev. B 49, 12975–12983 (1994).

    Article  ADS  Google Scholar 

  32. Chen, Q., Stajic, J., Tan, S. & Levin, K. BCS–BEC crossover: From high temperature superconductors to ultracold superfluids. Phys. Rep. 412, 1–88 (2005).

    Article  ADS  Google Scholar 

  33. Burovski, E., Prokof’ev, N., Svistunov, B. & Troyer, M. Critical temperature and thermodynamics of attractive fermions at unitarity. Phys. Rev. Lett. 96, 160402 (2006).

    Article  ADS  Google Scholar 

  34. Bulgac, A., Drut, J. & Magierski, P. Spin 1/2 fermions in the unitary regime: A superfluid of a new type. Phys. Rev. Lett. 96, 090404 (2006).

    Article  ADS  MATH  Google Scholar 

  35. Hu, H., Liu, X. & Drummond, P. Equation of state of a superfluid Fermi gas in the BCS–BEC crossover. Europhys. Lett. 74, 574–580 (2006).

    Article  ADS  Google Scholar 

  36. Haussmann, R., Rantner, W., Cerrito, S. & Zwerger, W. Thermodynamics of the BCS–BEC crossover. Phys. Rev. A 75, 023610 (2007).

    Article  ADS  Google Scholar 

  37. Combescot, R., Alzetto, F. & Leyronas, X. Particle distribution tail and related energy formula. Phys. Rev. A 79, 053640 (2009).

    Article  ADS  Google Scholar 

  38. Luo, L., Clancy, B., Joseph, J., Kinast, J. & Thomas, J. Measurement of the entropy and critical temperature of a strongly interacting Fermi gas. Phys. Rev. Lett. 98, 080402 (2007).

    Article  ADS  Google Scholar 

  39. Horikoshi, M., Nakajima, S., Ueda, M. & Mukaiyama, T. Measurement of universal thermodynamic functions for a unitary Fermi gas. Science 327, 442–445 (2010).

    Article  ADS  Google Scholar 

  40. Nascimbène, S., Navon, N., Jiang, K., Chevy, F. & Salomon, C. Exploring the thermodynamics of a universal Fermi gas. Nature 463, 1057–1060 (2010).

    Article  ADS  Google Scholar 

  41. Van Houcke, K. et al. Feynman diagrams versus Feynman quantum emulator. Preprint at http://arxiv.org/abs/1110.3747 (2011).

  42. Rupak, G. Universality in a 2-component Fermi system at finite temperature. Phys. Rev. Lett. 98, 090403 (2007).

    Article  ADS  Google Scholar 

  43. Liu, X., Hu, H. & Drummond, P. Virial expansion for a strongly correlated Fermi gas. Phys. Rev. Lett. 102, 160401 (2009).

    Article  ADS  Google Scholar 

  44. Rakshit, D., Daily, K. & Blume, D. Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient. Preprint at http://arxiv.org/abs/1106.5958 (2011).

  45. Kohstall, C. et al. Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture. Preprint at http://arxiv.org/abs/1112.0020 (2011).

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

    Article  ADS  Google Scholar 

  47. Petsas, K., Coates, A. & Grynberg, G. Crystallography of optical lattices. Phys. Rev. A 50, 5173–5189 (1994).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  49. Sebby-Strabley, J., Anderlini, M., Jessen, P. & Porto, J. Lattice of double wells for manipulating pairs of cold atoms. Phys. Rev. A 73, 033605 (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  52. 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. Preprint at http://arxiv.org/abs/1111.5020 (2011).

  53. Jo, G-B. et al. Ultracold atoms in a tunable optical kagome lattice. Phys. Rev. Lett. 108, 045305 (2011).

    Article  ADS  Google Scholar 

  54. Grossmann, F., Dittrich, T., Jung, P. & Hänggi, P. Coherent destruction of tunneling. Phys. Rev. Lett. 67, 516–519 (1991).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  59. Jaksch, D. & Zoller, P. The cold atoms Hubbard toolbox. Ann. Phys. 315, 52–79 (2005).

    Article  ADS  MATH  Google Scholar 

  60. Lewenstein, M. et al. Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007).

    Article  ADS  Google Scholar 

  61. Esslinger, T. Fermi–Hubbard physics with atoms in an optical lattice. Annu. Rev. Condens. Mater. Phys. 1, 129–152 (2010).

    Article  ADS  Google Scholar 

  62. Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989).

    Article  ADS  Google Scholar 

  63. Jaksch, D., Bruder, C., Cirac, J., Gardiner, C. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998).

    Article  ADS  Google Scholar 

  64. Greiner, M., Mandel, O., Esslinger, T., Hänsch, 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).

    Article  ADS  Google Scholar 

  65. Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010).

    Article  ADS  Google Scholar 

  66. Mark, M. et al. Precision measurements on a tunable Mott insulator of ultracold atoms. Phys. Rev. Lett. 107, 175301 (2011).

    Article  ADS  Google Scholar 

  67. Jördens, R., Strohmaier, N., Günter, K., Moritz, H. & Esslinger, T. A Mott Insulator of fermionic Atoms in an optical lattice. Nature 455, 204–207 (2008).

    Article  ADS  Google Scholar 

  68. Schneider, U. et al. Metallic and insulating phases of repulsively interacting fermions in a 3D optical lattice. Science 322, 1520–1525 (2008).

    Article  ADS  Google Scholar 

  69. Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, 1994).

    Book  Google Scholar 

  70. Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).

    Article  ADS  Google Scholar 

  71. Hazzard, K., Gurarie, V., Hermele, M. & Rey, A. High temperature thermodynamics of fermionic alkaline earth atoms in optical lattices. Preprint at http://arxiv.org/abs/1011.0032 (2010).

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

    Article  ADS  Google Scholar 

  73. Corboz, P., Läuchli, A., Penc, K., Troyer, M. & Mila, F. Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice. Phys. Rev. Lett. 107, 215301 (2011).

    Article  ADS  Google Scholar 

  74. Hermele, M., Gurarie, V. & Rey, A. Mott insulators of ultracold fermionic alkaline earth atoms: Underconstrained magnetism and chiral spin liquid. Phys. Rev. Lett. 103, 135301 (2009).

    Article  ADS  Google Scholar 

  75. Pichler, H., Daley, A. & Zoller, P. Nonequilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission. Phys. Rev. A 82, 063605 (2010).

    Article  ADS  Google Scholar 

  76. 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).

    Article  ADS  Google Scholar 

  77. Zimmermann, B., Müller, T., Meineke, J., Esslinger, T. & Moritz, H. High-resolution imaging of ultracold fermions in microscopically tailored optical potentials. New J. Phys. 13, 043007 (2011).

    Article  ADS  Google Scholar 

  78. Nelson, K., Li, X. & Weiss, D. Imaging single atoms in a three-dimensional array. Nature Phys. 3, 556–560 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  81. Gericke, T., Würtz, P., Reitz, D., Langen, T. & Ott, H. High-resolution scanning electron microscopy of an ultracold quantum gas. Nature Phys. 4, 949–953 (2008).

    Article  ADS  Google Scholar 

  82. Berg, E., Dalla Torre, E., Giamarchi, T. & Altman, E. Rise and fall of hidden string order of lattice bosons. Phys. Rev. B 77, 245119 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  85. Löw, R. et al. An experimental and theoretical guide to strongly interacting Rydberg gases. Preprint at http://arxiv.org/abs/1202.2871 (2012).

  86. Carr, L., DeMille, D., Krems, R. & Ye, J. Cold and ultracold molecules: science, technology and applications. New J. Phys. 11, 055049 (2009).

    Article  ADS  Google Scholar 

  87. Dalla Torre, E. G., Berg, E. & Altman, E. Hidden Order in 1D Bose Insulators. Phys. Rev. Lett. 97, 260401 (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  89. Ho, T-L. & Zhou, Q. Universal cooling scheme for quantum simulation. Preprint at http://arxiv.org/abs/0911.5506 (2009).

  90. Bernier, J-S. et al. Cooling fermionic atoms in optical lattices by shaping the confinement. Phys. Rev. A 79, 061601(R) (2009).

    Article  ADS  Google Scholar 

  91. Rabl, P., Daley, A., Fedichev, P., Cirac, J. & Zoller, P. Defect-suppressed atomic crystals in an optical lattice. Phys. Rev. Lett. 91, 110403 (2003).

    Article  ADS  Google Scholar 

  92. Bakr, W. S. et al. Orbital excitation blockade and algorithmic cooling in quantum gases. Nature 480, 500–503 (2011).

    Article  ADS  Google Scholar 

  93. Sachdev, S., Sengupta, K. & Girvin, S. Mott insulators in strong electric fields. Phys. Rev. B 66, 075128 (2002).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  95. Ma, R. et al. Photon-assisted tunneling in a biased strongly correlated Bose gas. Phys. Rev. Lett 107, 095301 (2011).

    Article  ADS  Google Scholar 

  96. Pielawa, S., Kitagawa, T., Berg, E. & Sachdev, S. Correlated phases of bosons in tilted frustrated lattices. Phys. Rev. B 83, 205135 (2011).

    Article  ADS  Google Scholar 

  97. Cooper, N. R. Rapidly rotating atomic gases. Adv. Phys. 57, 539–616 (2008).

    Article  ADS  Google Scholar 

  98. Landau, L. D. & Lifshitz, E. M. Quantum Mechanics: Non-Relativistic Theory (Pergamon Press, 1977).

    MATH  Google Scholar 

  99. Laughlin, R. B. Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983).

    Article  ADS  Google Scholar 

  100. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

    Article  ADS  Google Scholar 

  101. Fetter, A. L. Rotating trapped Bose–Einstein condensates. Rev. Mod. Phys. 81, 647–691 (2009).

    Article  ADS  Google Scholar 

  102. Schweikhard, V., Coddington, I., Engels, P., Mogendorff, V. P. & Cornell, E. A. Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level. Phys. Rev. Lett. 92, 040404 (2004).

    Article  ADS  Google Scholar 

  103. Roncaglia, M., Rizzi, M. & Cirac, J. I. Pfaffian state generation by strong three-body dissipation. Phys. Rev. Lett. 104, 096803 (2010).

    Article  ADS  Google Scholar 

  104. Roncaglia, M., Rizzi, M. & Dalibard, J. From rotating atomic rings to quantum Hall states. Sci. Rep. 1, 1–6 (2011).

    Article  Google Scholar 

  105. Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. A 392, 45–57 (1984).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  106. Dum, R. & Olshanii, M. Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice. Phys. Rev. Lett. 76, 1788–1791 (1996).

    Article  ADS  Google Scholar 

  107. Juzeliunas, G. & Öhberg, P. Slow light in degenerate Fermi gases. Phys. Rev. Lett. 93, 033602 (2004).

    Article  ADS  Google Scholar 

  108. Juzeliunas, G., Ruseckas, J., Öhberg, P. & Fleischhauer, M. Light-induced effective magnetic fields for ultracold atoms in planar geometries. Phys. Rev. A 73, 025602 (2006).

    Article  ADS  Google Scholar 

  109. Dalibard, J., Gerbier, F., Juzeliūnas, G. & Öhberg, P. Colloquium : Artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523–1543 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  111. Lin, Y., Jiménez-Garcia, K. & Spielman, I. B. Spin-orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  113. Qi, X-L. & Zhang, S-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    Article  ADS  Google Scholar 

  114. Zhang, C., Tewari, S., Lutchyn, R. M. & Das Sarma, S. p x+i p y superfluid from s-wave interactions of fermionic cold atoms. Phys. Rev. Lett. 101, 160401 (2008).

    Article  ADS  Google Scholar 

  115. Goldman, N. et al. Realistic time-reversal invariant topological insulators with neutral atoms. Phys. Rev. Lett. 105, 255302 (2010).

    Article  ADS  Google Scholar 

  116. Béri, B. & Cooper, N. R. topological insulators in ultracold atomic gases. Phys. Rev. Lett. 107, 145301 (2011).

    Article  ADS  Google Scholar 

  117. Jaksch, D. & Zoller, P. Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms. New J. Phys. 5, 56 (2003).

    Article  ADS  Google Scholar 

  118. Mueller, E. J. Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids. Phys. Rev. A 70, 041603 (2004).

    Article  ADS  Google Scholar 

  119. Sørensen, A. S., Demler, E. & Lukin, M. D. Fractional quantum Hall states of atoms in optical lattices. Phys. Rev. Lett. 94, 086803 (2005).

    Article  ADS  Google Scholar 

  120. Lim, L-K., Smith, C. M. & Hemmerich, A. Staggered-vortex superfluid of ultracold Bosons in an optical lattice. Phys. Rev. Lett. 100, 130402 (2008).

    Article  ADS  Google Scholar 

  121. Ruostekoski, J., Dunne, G. V. & Javanainen, J. Particle number fractionalization of an atomic Fermi–Dirac gas in an optical lattice. Phys. Rev. Lett. 88, 180401 (2002).

    Article  ADS  Google Scholar 

  122. Hofstadter, D. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239–2249 (1976).

    Article  ADS  Google Scholar 

  123. Pannetier, B., Chaussy, J., Rammal, R. & Villegier, J. C. Experimental fine tuning of frustration: Two-dimensional superconducting network in a magnetic field. Phys. Rev. Lett. 53, 1845–1848 (1984).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  125. Cooper, N. R. Optical flux lattices for ultracold atomic gases. Phys. Rev. Lett. 106, 175301 (2011).

    Article  ADS  Google Scholar 

  126. Cooper, N. R. & Dalibard, J. Optical flux lattices for two-photon dressed states. Europhys. Lett. 95, 66004 (2011).

    Article  ADS  Google Scholar 

  127. Ruseckas, J., Juzeliūnas, G., Öhberg, P. & Fleischhauer, M. Non-abelian gauge potentials for ultracold atoms with degenerate dark states. Phys. Rev. Lett. 95, 010404 (2005).

    Article  ADS  Google Scholar 

  128. Osterloh, K., Baig, M., Santos, L., Zoller, P. & Lewenstein, M. Cold atoms in non-abelian gauge potentials: From the Hofstadter ‘Moth’ to lattice gauge theory. Phys. Rev. Lett. 95, 010403 (2005).

    Article  ADS  Google Scholar 

  129. Wilczek, F. & Zee, A. Appearance of gauge structure in simple dynamical systems. Phys. Rev. Lett. 52, 2111–2114 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  130. Goldman, N. Quantum Transport in Lattices Subjected to External Gauge Fields (VDM Verlag, 2009).

    Google Scholar 

  131. Büchler, H., Hermele, M., Huber, S., Fisher, M. & Zoller, P. Atomic quantum simulator for lattice gauge theories and ring exchange models. Phys. Rev. Lett. 95, 040402 (2005).

    Article  ADS  Google Scholar 

  132. Sanchez-Palencia, L. & Lewenstein, M. Disordered quantum gases under control. Nature Phys. 6, 87–95 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  134. Roati, G. et al. Anderson localization of a non-interacting Bose-Einstein condensate. Nature 453, 895–898 (2008).

    Article  ADS  Google Scholar 

  135. Kondov, S. S., McGehee, W. R., Zirbel, J. J. & DeMarco, B. Three-dimensional Anderson localization of ultracold matter. Science 334, 66–68 (2011).

    Article  ADS  Google Scholar 

  136. Castin, Y. & Pricoupenko, L. (eds) The few body problem. C. R. Phys. 12, 1–109 (2011).

  137. Trotzky, S. et al. Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas. Nature Phys. 8, 325–330 (2012).

    Article  ADS  Google Scholar 

  138. Polkovnikov, A., Sengupta, K., Silva, A. & Vengalattore, M. Colloquium: Nonequilibrium dynamics of closed interacting quantum systems. Rev. Mod. Phys. 83, 863–883 (2011).

    ADS  Google Scholar 

  139. Lamacraft, A. & Moore, J. Potential insights into non-equilibrium behavior from atomic physics. Preprint at http://arXiv.org/abs/1106.3567 1–24 (2011).

  140. Pilati, S. & Giorgini, S. Phase separation in a polarized Fermi gas at zero temperature. Phys. Rev. Lett. 100, 030401 (2008).

    Article  ADS  Google Scholar 

  141. Fuchs, J., Leyronas, X. & Combescot, R. Hydrodynamic modes of a one-dimensional trapped Bose gas. Phys. Rev. A 68, 043610 (2003).

    Article  ADS  Google Scholar 

  142. Ho, T. & Zhou, Q. Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases. Nature Phys. 6, 131–134 (2009).

    Article  ADS  Google Scholar 

  143. Spiegelhalder, F. et al. Collisional stability of 40K immersed in a strongly interacting Fermi gas of 6Li. Phys. Rev. Lett. 103, 223203 (2009).

    Article  ADS  Google Scholar 

  144. DePue, M. T. M., McCormick, C., Winoto, S. L., Oliver, S. & Weiss, D. D. S. Unity Occupation of Sites in a 3D Optical Lattice. Phys. Rev. Lett. 82, 2262–2265 (1999).

    Article  ADS  Google Scholar 

  145. Gerbier, F. & Dalibard, J. Gauge fields for ultracold atoms in optical superlattices. New J. Phys. 12, 033007 (2010).

    Article  ADS  Google Scholar 

  146. Möller, G. & Cooper, N. Condensed ground states of frustrated Bose–Hubbard models. Phys. Rev. A 82, 063625 (2010).

    Article  ADS  Google Scholar 

  147. Lim, L-K., Hemmerich, A. & Smith, C. M. Artificial staggered magnetic field for ultracold atoms in optical lattices. Phys. Rev. A 81, 023404 (2010).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank P. Zoller and E. Altman for many useful discussions during the writing of this review article.

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Authors and Affiliations

  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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  1. Immanuel Bloch
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Correspondence to Immanuel Bloch.

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Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nature Phys 8, 267–276 (2012). https://doi.org/10.1038/nphys2259

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