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Ultracold quantum gases in optical lattices


Artificial crystals of light, consisting of hundreds of thousands of optical microtraps, are routinely created by interfering optical laser beams. These so-called optical lattices act as versatile potential landscapes to trap ultracold quantum gases of bosons and fermions. They form powerful model systems of quantum many-body systems in periodic potentials for probing nonlinear wave dynamics and strongly correlated quantum phases, building fundamental quantum gates or observing Fermi surfaces in periodic potentials. Optical lattices represent a fast-paced modern and interdisciplinary field of research.

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Figure 1: Optical lattice potentials formed by superimposing two or three orthogonal standing waves.
Figure 2: Optical lattice potentials.
Figure 3: Adiabatic mapping of crystal momentum onto free-space momentum of an atom.
Figure 4: Nonlinear dynamics for a BEC in a double-well system.
Figure 5: Dynamical instability of a BEC in a periodic potential.
Figure 6: Transition from a superfluid to a Mott insulator.
Figure 7: Observing Fermi surfaces.
Figure 8: Quantum noise correlations in atom clouds released from an optical lattice.


  1. 1

    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).

    ADS  Article  Google Scholar 

  2. 2

    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).

    ADS  Article  Google Scholar 

  3. 3

    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).

    ADS  Article  Google Scholar 

  4. 4

    Orzel, C., Tuchman, A. K., Fenselau, M. L., Yasuda, M. & Kasevich, M. A. Squeezed states in a Bose-Einstein condensate. Science 291, 2386–2389 (2001).

    ADS  Article  Google Scholar 

  5. 5

    Girardeau, M. Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys. 1, 516–523 (1960).

    ADS  MathSciNet  Article  Google Scholar 

  6. 6

    Paredes, B. et al. Tonks–Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004).

    ADS  Article  Google Scholar 

  7. 7

    Kinoshita, T., Wenger, T. & Weiss, D. S. Observation of a one-dimensional Tonks-Girardeau gas. Science 305, 1125–1128 (2004).

    ADS  Article  Google Scholar 

  8. 8

    deMarco, B. & Jin, D. S. Onset of Fermi degeneracy in a trapped atomic gas. Science 285, 1703–1706 (1999).

    Article  Google Scholar 

  9. 9

    Truscott, A. G., Strecker, K. E., McAlexander, W. I., Partridge, G. B. & Hulet, R. G. Observation of Fermi pressure in a gas of trapped atoms. Science 291, 2570–2572 (2001).

    ADS  Article  Google Scholar 

  10. 10

    Regal, C., Greiner, M. & Jin, D. S. Observation of resonance condensation of fermionic atom pairs. Phys. Rev. Lett. 92, 040403 (2004).

    ADS  Article  Google Scholar 

  11. 11

    Chin, C. et al. Observation of the pairing gap in a strongly interacting Fermi gas. Science 305, 1128–1130 (2004).

    ADS  Article  Google Scholar 

  12. 12

    Zwierlein, M. W., Abo-Shaeer, J. R., Schirotzek, A., Schunck, C. H. & Ketterle, W. Vortices and superfluidity in a strongly interacting Fermi gas. Nature 435, 1047–1051 (2005).

    ADS  Article  Google Scholar 

  13. 13

    Bloch, I. Quantum gases in optical lattices. Phys. World 17, 25–29 (2004).

    ADS  Article  Google Scholar 

  14. 14

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

    ADS  Article  Google Scholar 

  15. 15

    Ryu, C. et al. Raman-induced oscillation between an atomic and a molecular quantum gas. Prepint at (2005).

  16. 16

    Feynman, R. P. Quantum mechanical computers. Opt. News 11, 11–20 (1985).

    Article  Google Scholar 

  17. 17

    Feynman, R. P. Quantum mechanical computers. Found. Phys. 16, 507–531 (1986).

    ADS  MathSciNet  Article  Google Scholar 

  18. 18

    Grimm, R., Weidemüller, M. & Ovchinnikov, Y. B. Optical dipole traps for neutral atoms. Adv. At. Mol. Opt. Phys. 42, 95–170 (2000).

    ADS  Article  Google Scholar 

  19. 19

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

    ADS  Article  Google Scholar 

  20. 20

    Santos, L. et al. Atomic quantum gases in Kagomé lattices. Phys. Rev. Lett. 93, 030601 (2004).

    ADS  Article  Google Scholar 

  21. 21

    Kastberg, A., Phillips, W. D., Rolston, S. L. & Spreeuw, R. J. C. Adiabatic cooling of cesium to 700 nK in an optical lattice. Phys. Rev. Lett. 74, 1542–1545 (1995).

    ADS  Article  Google Scholar 

  22. 22

    Greiner, M., Bloch, I., Mandel, O., Hänsch, T. W. & Esslinger, T. Bose-Einstein condensates in 1D and 2D optical lattices. Appl. Phys. B 73, 769–772 (2001).

    ADS  Article  Google Scholar 

  23. 23

    Bloch, I. & Greiner, M. Exploring quantum matter with ultracold atoms in optical lattices. Adv. At. Mol. Phys. (in the press).

  24. 24

    Köhl, M., Moritz, H., Stöferle, T., Günter, K. & Esslinger, T. Fermionic atoms in a 3D optical lattice: Observing Fermi-surfaces, dynamics and interactions. Phys. Rev. Lett. 94, 080403 (2004).

    Article  Google Scholar 

  25. 25

    Anderson, B. P. & Kasevich, M. A. Macroscopic quantum interference from atomic tunnel arrays. Science 282, 1686–1689 (1998).

    ADS  Article  Google Scholar 

  26. 26

    Cataliotti, F. S. et al. Josephson junction arrays with Bose-Einstein condensates. Science 293, 843–846 (2001).

    ADS  Article  Google Scholar 

  27. 27

    Albiez, M. et al. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. Phys. Rev. Lett. 95, 010402 (2005).

    ADS  Article  Google Scholar 

  28. 28

    Josephson, B. D. Possible new effects in superconductive tunnelling. Phys. Lett. 1, 251–253 (1962).

    ADS  Article  Google Scholar 

  29. 29

    Likharev, K. K. Superconducting weak links. Rev. Mod. Phys. 51, 101–159 (1979).

    ADS  Article  Google Scholar 

  30. 30

    Pereverzev, S. V., Loshak, A., Backhaus, S., Davis, J. C. & Packard, R. E. Quantum oscillations between two weakly coupled reservoirs of superfluid 3He. Nature 388, 449–451 (1997).

    ADS  Article  Google Scholar 

  31. 31

    Sukhatme, K., Mukharsky, Y., Chui, T. & Pearson, D. Observation of the ideal Josephson effect in superfluid 4He. Nature 411, 280–283 (2001).

    ADS  Article  Google Scholar 

  32. 32

    Fallani, L. et al. Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice. Phys. Rev. Lett. 93, 140406 (2004).

    ADS  Article  Google Scholar 

  33. 33

    Wu, B. & Niu, Q. Landau and dynamical instabilities of the superflow of Bose-Einstein condensates in optical lattices. Phys. Rev. A 64, 061603 (2001).

    ADS  Article  Google Scholar 

  34. 34

    Smerzi, A., Trombettoni, A., Kevrekidis, P. G. & Bishop, A. R. Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates. Phys. Rev. Lett. 89, 170402 (2002).

    ADS  Article  Google Scholar 

  35. 35

    Pitaevskii, L. P. & Stringari, S. Bose-Einstein Condensation (Oxford Science, Oxford, 2003).

    MATH  Google Scholar 

  36. 36

    Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985).

    ADS  Article  Google Scholar 

  37. 37

    Zurek, W. H., Dorner, U. & Zoller, P. Dynamics of a quantum phase transition. Phys. Rev. Lett. 95, 105701 (2005).

    ADS  Article  Google Scholar 

  38. 38

    Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004).

    ADS  Article  Google Scholar 

  39. 39

    Fertig, C. D. et al. Strongly inhibited transport of a degenerate 1D Bose gas in a lattice. Phys. Rev. Lett. 94, 120403 (2005).

    ADS  Article  Google Scholar 

  40. 40

    Polkovnikov, A. & Wang, D. -W. Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices. Phys. Rev. Lett. 93, 070401 (2004).

    ADS  Article  Google Scholar 

  41. 41

    Laburthe-Tolra, B. et al. Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas. Phys. Rev. Lett. 92, 190401 (2004).

    Article  Google Scholar 

  42. 42

    Lieb, E. H. & Liniger, W. Exact analysis of an interacting Bose gas. The general solution and the ground state. Phys. Rev. B 130, 1605–1616 (1963).

    ADS  MathSciNet  Article  Google Scholar 

  43. 43

    Giamarchi, T. Quantum Physics in One Dimension (Oxford Science, Oxford, 2004).

    MATH  Google Scholar 

  44. 44

    Ott, H. et al. Collisionally induced transport in periodic potentials. Phys. Rev. Lett. 92, 160601 (2004).

    ADS  Article  Google Scholar 

  45. 45

    Pezzè, L. et al. Insulating behavior of a trapped Fermi gas. Phys. Rev. Lett. 93, 120401 (2004).

    ADS  Article  Google Scholar 

  46. 46

    Kuklov, A. & Svistunov, B. Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice. Phys. Rev. Lett. 90, 100401 (2003).

    ADS  Article  Google Scholar 

  47. 47

    Kuklov, A., Prokof'ev, N. V. & Svistunov, B. Commensurate two-component bosons in an optical lattice: Ground state phase diagram. Phys. Rev. Lett. 92, 050402 (2004).

    ADS  Article  Google Scholar 

  48. 48

    Paredes, B. & Cirac, J. I. From Cooper pairs to Luttinger liquids with bosonic atoms in optical lattices. Phys. Rev. Lett. 90, 150402 (2003).

    ADS  Article  Google Scholar 

  49. 49

    Recati, A., Fedichev, P. O., Zwerger, W., von Delft, J. & Zoller, P. Atomic quantum dots coupled to a reservoir of a superfluid Bose-Einstein condensate. Phys. Rev. Lett. 94, 040404 (2005).

    ADS  Article  Google Scholar 

  50. 50

    Micheli, A., Daley, A. J., Jaksch, D. & Zoller, P. Single atom transistor in a 1D optical lattice. Phys. Rev. Lett. 93, 140408 (2004).

    ADS  Article  Google Scholar 

  51. 51

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

    ADS  Article  Google Scholar 

  52. 52

    Altman, E., Hofstetter, W., Demler, E. & Lukin, M. D. Phase diagram of two-component bosons on an optical lattice. New J. Phys. 5, 113 (2003).

    ADS  Article  Google Scholar 

  53. 53

    Roth, R. & Burnett, K. Ultracold bosonic atoms in two-color disordered optical superlattices. J. Opt. B 5, S50–S54 (2003).

    ADS  Article  Google Scholar 

  54. 54

    Roth, R. & Burnett, K. Phase diagram of bosonic atoms in two-color superlattices. Phys. Rev. A 68, 023604 (2003).

    ADS  Article  Google Scholar 

  55. 55

    Damski, B., Zakrzwewski, J., Santos, L., Zoller, P. & Lewenstein, M. Atomic Bose and Anderson glasses in optical lattices. Phys. Rev. Lett. 91, 080403 (2003).

    ADS  Article  Google Scholar 

  56. 56

    Sanpera, A., Kantian, A., Sanchez-Palencia, L., Zakrzwewski, J. & Lewenstein, M. Atomic Fermi-Bose mixtures in inhomogeneous and random lattices: From Fermi glass to quantum spin glass and quantum percolation. Phys. Rev. Lett. 93, 040401 (2004).

    ADS  Article  Google Scholar 

  57. 57

    Lye, J. E. et al. A Bose-Einstein condensate in a random potential. Phys. Rev. Lett. 95, 070401 (2005).

    ADS  Article  Google Scholar 

  58. 58

    Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).

    ADS  Article  Google Scholar 

  59. 59

    Anderson, P. W. et al. The physics behind high-temperature superconducting cuprates: the 'plain vanilla' version of RVB. J. Phys. Cond. Mat. 16, R755–R769 (2004).

    Article  Google Scholar 

  60. 60

    Hofstetter, W., Cirac, J. I., Zoller, P., Demler, E. & Lukin, M. D. High-temperature superfluidity of fermionic atoms in optical lattices. Phys. Rev. Lett. 89, 220407 (2002).

    ADS  Article  Google Scholar 

  61. 61

    Roati, G. et al. Atom interferometry with trapped Fermi gases. Phys. Rev. Lett. 92, 230402 (2004).

    ADS  Article  Google Scholar 

  62. 62

    Büchler, H. P. & Blatter, G. Phase separation of atomic Bose-Fermi mixtures in an optical lattice. Phys. Rev. A 69, 063603 (2004).

    ADS  Article  Google Scholar 

  63. 63

    Albus, A., Illuminati, F. & Eisert, J. Mixtures of bosonic and fermionic atoms in optical lattices. Phys. Rev. A 68, 023606 (2003).

    ADS  Article  Google Scholar 

  64. 64

    Roth, R. & Burnett, K. Quantum phases of atomic boson-fermion mixtures in optical lattices. Phys. Rev. A 69, 021601(R) (2004).

    ADS  Article  Google Scholar 

  65. 65

    Lewenstein, M., Santos, L., Baranov, M. A. & Fehrmann, H. Atomic Bose-Fermi mixtures in an optical lattice. Phys. Rev. Lett. 92, 050401 (2004).

    ADS  Article  Google Scholar 

  66. 66

    Altman, E., Demler, E. & Lukin, M. D. Probing many-body states of ultracold atoms via noise correlations. Phys. Rev. A 70, 013603 (2004).

    ADS  Article  Google Scholar 

  67. 67

    Greiner, M., Regal, C. A., Stewart, J. T. & Jin, D. S. Probing pair-correlated fermionic atoms through correlations in atom shot noise. Phys. Rev. Lett. 110401 (2005).

  68. 68

    Fölling, S. et al. Spatial quantum noise interferometry in expanding ultracold atomic gases. Nature 434, 481–484 (2005).

    ADS  Article  Google Scholar 

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

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