Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Artificial Gauge Fields with Ultracold Atoms in Optical Lattices

Part of the book series: Springer Theses ((Springer Theses))

  • 1265 Accesses

Abstract

The topic of this thesis is at the interface between condensed matter physics and ultracold quantum gases. The introductory chapter gives a brief overview over topological quantum states of matter and important experimental works in the field of ultracold atoms that enable a study of related phenomena with ultracold atoms in optical lattices.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. P.W. Anderson, Basic Notions of Condensed Matter Physics (Westview Press, Boulder, 1997)

    Google Scholar 

  2. K. von Klitzing, G. Dorda, M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Phys. Rev. Lett. 45, 494–497 (1980)

    Google Scholar 

  3. K. von Klitzing, The quantized Hall effect. Rev. Mod. Phys. 58, 519–531 (1986)

    Google Scholar 

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

    Google Scholar 

  5. J.E. Moore, The birth of topological insulators. Nature 464, 194–198 (2010)

    Google Scholar 

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

    Google Scholar 

  7. R.B. Laughlin, Quantized Hall conductivity in two dimensions. Phys. Rev. B 23, 5632–5633 (1981)

    Google Scholar 

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

    Google Scholar 

  9. J.B. Listing, Vorstudien zur Topologie (Vanderhoeck und Ruprecht, Göttingen, 1848)

    Google Scholar 

  10. Y. Hatsugai, Chern number and edge states in the integer quantum Hall effect. Phys. Rev. Lett. 71, 3697–3700 (1993)

    Google Scholar 

  11. Y. Hatsugai, Edge states in the integer Quantum Hall effect and the Riemann surface of the Bloch function. Phys. Rev. B 48, 11851–11862 (1993)

    Google Scholar 

  12. X.-L. Qi, Y.-S. Wu, S.-C. Zhang, General theorem relating the bulk topological number to edge states in two-dimensional insulators. Phys. Rev. B 74, 045125 (2006)

    Google Scholar 

  13. E.J. Bergholtz, Z. Liu, Topological flat band models and fractional Chern insulators. Int. J. Mod. Phys. B 27, 1330017 (2013)

    Google Scholar 

  14. F.D.M. Haldane, Model for a Quantum Hall effect without landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015–2018 (1988)

    Google Scholar 

  15. C.L. Kane, E.J. Mele, Quantum Spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005)

    Google Scholar 

  16. B.A. Bernevig, S.-C. Zhang, Quantum Spin Hall effect. Phys. Rev. Lett. 96, 106802 (2006)

    Google Scholar 

  17. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.-L. Qi, S.-C. Zhang, Quantum Spin hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007)

    Google Scholar 

  18. M. König, H. Buhmann, L.W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, S.-C. Zhang, The Quantum Spin Hall effect: theory and experiment. J. Phys. Soc. Jpn. 77, 031007 (2008)

    Google Scholar 

  19. A. Roth, C. Brüne, H. Buhmann, L.W. Molenkamp, J. Maciejko, X.-L. Qi, S.-C. Zhang, Nonlocal transport in the quantum spin Hall state. Science 325, 294–297 (2009)

    Google Scholar 

  20. L. Fu, C.L. Kane, E.J. Mele, Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007)

    Google Scholar 

  21. J.E. Moore, L. Balents, Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306 (2007)

    Google Scholar 

  22. R. Roy, Topological phases and the quantum spin Hall effect in three dimensions. Phys. Rev. B 79, 195322 (2009)

    Google Scholar 

  23. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y.S. Hor, R.J. Cava, M.Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008)

    Google Scholar 

  24. Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009)

    Google Scholar 

  25. D.C. Tsui, H.L. Stormer, A.C. Gossard, Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982)

    Google Scholar 

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

    Google Scholar 

  27. S.A. Parameswaran, R. Roy, S.L. Sondhi, Fractional quantum Hall physics in topological flat bands. C. R. Phys. 14, 816–839 (2013)

    Google Scholar 

  28. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma, Q.-K. Xue, Experimental observation of the quantum anomalous Hall Effect in a magnetic topological insulator. Science 340, 167–170 (2013)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  34. S. Fölling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. Müller, I. Bloch, Direct observation of second-order atom tunnelling. Nature 448, 1029–1132 (2007)

    Google Scholar 

  35. C. Becker, P. Soltan-Panahi, J. Kronjäger, S. Dörscher, K. Bongs, K. Sengstock, Ultracold quantum gases in triangular optical lattices. New. J. Phys. 12, 065025 (2010)

    Google Scholar 

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

    Google Scholar 

  37. G.-B. Jo, J. Guzman, C.K. Thomas, P. Hosur, A. Vishwanath, D.M. Stamper-Kurn, Ultracold atoms in a tunable optical kagome lattice. Phys. Rev. Lett. 108, 045305 (2012)

    Google Scholar 

  38. J. Hubbard, Electron correlations in narrow energy bands. Proc. R. Soc. Lond. 276, 238–257 (1963)

    Google Scholar 

  39. D. Jaksch, P. Zoller, The cold atom Hubbard toolbox. Ann. Phys. 315, 52–79 (2005)

    Google Scholar 

  40. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De), U. Sen, Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  49. W.S. Bakr, J.I. Gillen, A. Peng, S. Fölling, M. Greiner, A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74–77 (2009)

    Google Scholar 

  50. J.F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, S. Kuhr, Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010)

    Google Scholar 

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

    Google Scholar 

  52. M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauß, C. Gross, L. Mazza, M.C. Bañuls, L. Pollet, I. Bloch, S. Kuhr, Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators. Science 334, 200–203 (2011)

    Google Scholar 

  53. C. Weitenberg, M. Endres, J.F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, S. Kuhr, Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011)

    Google Scholar 

  54. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, T. Esslinger, Experimental realisation of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014)

    Google Scholar 

  55. T. Oka, H. Aoki, Photovoltaic Hall effect in graphene. Phys. Rev. B 79, 081406 (2009)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  59. N. Goldman, G. Juzeli\(\bar{\text{ u }}\)nas, P. Öhberg, I.B. Spielman, Light-induced gauge fields for ultracold atoms.Rep. Prog. Phys. 77, 126401 (2014)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  63. A.R. Kolovsky, Creating artificial magnetic fields for cold atoms by photon-assisted tunneling. Europhys. Lett. 93, 20003 (2011)

    Google Scholar 

  64. C.E. Creffield, F. Sols, Comment on “Creating artificial magnetic fields for cold atoms by photon-assisted tunneling” by A.R. Kolovsky. Europhys. Lett. 101, 40001 (2013)

    Google Scholar 

  65. A. Bermudez, T. Schaetz, D. Porras, Synthetic gauge fields for vibrational excitations of trapped ions. Phys. Rev. Lett. 107, 150501 (2011)

    Google Scholar 

  66. N. Goldman, J. Dalibard, M. Aidelsburger, N.R. Cooper, Periodically-driven quantum matter: the case of resonant modulations. Phys. Rev. A 91, 033632 (2015)

    Google Scholar 

  67. J. Struck, C. Ölschläger, R. Le Targat, P. Soltan-Panahi, A. Eckardt, M. Lewenstein, P. Windpassinger, K. Sengstock, Quantum simulation of frustrated classical magnetism in triangular optical lattices. Science 333, 996–999 (2011)

    Google Scholar 

  68. M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, I. Bloch, Experimental realization of strong effective magnetic fields in an optical lattice. Phys. Rev. Lett. 107, 255301 (2011)

    Google Scholar 

  69. M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, I. Bloch, Experimental realization of strong effective magnetic fields in optical superlattice potentials. Appl. Phys. B 113, 1–11 (2013)

    Google Scholar 

  70. M. Aidelsburger, M. Atala, M. Lohse, J.T. Barreiro, B. Paredes, I. Bloch, Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301 (2013)

    Google Scholar 

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

    Google Scholar 

  72. M. Atala, M. Aidelsburger, M. Lohse, J.T. Barreiro, B. Paredes, I. Bloch, Observation of chiral currents with ultracold atoms in bosonic ladders. Nat. Phys. 10, 588–593 (2014)

    Google Scholar 

  73. M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J.T. Barreiro, S. Nascimbène, N.R. Cooper, I. Bloch, N. Goldman, Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11, 162–166 (2015)

    Google Scholar 

  74. M.Y. Azbel, Energy spectrum of a conduction electron in a magnetic field. JETP 19 (1964)

    Google Scholar 

  75. P.G. Harper, Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. A 68, 874 (1955)

    Google Scholar 

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

    Google Scholar 

  77. N. Goldman, I. Satija, P. Nikolic, A. Bermudez, M.A. Martin-Delgado, M. Lewenstein, I.B. Spielman, Realistic time-reversal invariant topological insulators with neutral atoms. Phys. Rev. Lett. 105, 255302 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ludwig-Maximilians-Universität München, Munich, Germany

    Monika Aidelsburger

Authors
  1. Monika Aidelsburger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Monika Aidelsburger .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Aidelsburger, M. (2016). Introduction. In: Artificial Gauge Fields with Ultracold Atoms in Optical Lattices. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-25829-4_1

Download citation

Publish with us

Policies and ethics

Search

Navigation