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Disordered quantum gases under control

Nature Physics volume 6, pages 87–95 (2010)Cite this article

Abstract

When attempting to understand the role of disorder in condensed-matter physics, we face considerable experimental and theoretical difficulties, and many questions are still open. Two of the most challenging ones—debated for decades—concern the effect of disorder on superconductivity and quantum magnetism. We review recent progress in the field of ultracold atomic gases, which should pave the way towards the realization of versatile quantum simulators, which help solve these questions. In addition, ultracold gases offer original practical and conceptual approaches, which open new perspectives to the field of disordered systems.

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Figure 1: Experimental observation of Anderson localization of matter waves with Bose–Einstein condensates.
Figure 2: Effect of interactions in disordered Bose and Fermi gases.
Figure 3: The spin-glass problem.

References

  1. Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Saunders, 1976).

    MATH  Google Scholar 

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

    Book  Google Scholar 

  3. Lifshitz, E. M. & Pitaevskii, L. P. Landau and Lifshitz Course of Theoretical Physics: Statistical Physics, Part 2 (Pergamon, 1980).

    Google Scholar 

  4. Akkermans, E. & Montambaux, G. Mesoscopic Physics of Electrons and Photons (Cambridge Univ. Press, 2006).

    MATH  Google Scholar 

  5. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    Article  ADS  Google Scholar 

  6. Lee, P. A. & Ramakrishnan, T. V. Disordered electronic systems. Rev. Mod. Phys. 57, 287–337 (1985).

    ADS  Google Scholar 

  7. Wiersma, D. S., Bartolini, P., Lagendijk, A. & Righini, R. Localization of light in a disordered medium. Nature 390, 671–673 (1997).

    Article  ADS  Google Scholar 

  8. Störzer, M., Gross, P., Aegerter, C. M. & Maret, G. Observation of the critical regime near Anderson localization of light. Phys. Rev. Lett. 96, 063904 (2006).

    Article  ADS  Google Scholar 

  9. Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

    Article  ADS  Google Scholar 

  10. Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008).

    Article  ADS  Google Scholar 

  11. Chabanov, A. A., Stoytchev, M. & Genack, A. Z. Statistical signatures of photon localization. Nature 404, 850–853 (2000).

    Article  ADS  Google Scholar 

  12. Hu, H., Strybulevych, A., Skipetrov, S. E., van Tiggelen, B. A. & Page, J. H. Localization of ultrasound in a three-dimensional elastic network. Nature Phys. 4, 945–948 (2008).

    ADS  Google Scholar 

  13. Dalfovo, F., Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of Bose–Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463–512 (1999).

    Article  ADS  Google Scholar 

  14. Ketterle, W., Durfee, D. S. & Stamper-Kurn, D. M. in Proc. of the International School of Physics ‘Enrico Fermi’, Course CXL (eds Inguscio, M., Stringari, S. & Wieman, C. E.) (IOP Press, 1999); preprint at <http://arxiv.org/abs/cond-mat/9904034>.

    Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Ketterle, W. & Zwierlein, M. W. in Proc. of the International School of Physics ‘Enrico Fermi’, Course CLXIV (eds Inguscio, M., Ketterle, W. & Salomon, C.) (IOS Press, 2008); preprint at <http://arxiv.org/abs/0801.2500>.

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  18. Cirac, J. I. & Zoller, P. New frontiers in quantum information with atoms and ions. Phys. Today 57, 38–44 (2004).

    Article  Google Scholar 

  19. 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).

    Article  ADS  Google Scholar 

  20. 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 

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

    Article  ADS  Google Scholar 

  22. 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  Google Scholar 

  23. 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 

  24. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006).

    Article  ADS  Google Scholar 

  28. Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature 448, 452–456 (2007).

    Article  ADS  Google Scholar 

  29. 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 

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

    Article  ADS  Google Scholar 

  31. Fallani, L., Fort, C. & Inguscio, M. Bose–Einstein condensates in disordered potentials. Adv. At. Mol. Opt. Phys. 56, 119–160 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. Roth, T. & Burnett, K. Ultracold bosonic atoms in disordered optical superlattices. J. Opt. B: Quant. Semiclass. Opt. 5, S50–S54 (2003).

    Article  ADS  Google Scholar 

  34. Sanchez-Palencia, L. et al. Anderson localization of expanding Bose–Einstein condensates in random potentials. Phys. Rev. Lett. 98, 210401 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. Clément, D. et al. Suppression of transport of an interacting elongated Bose–Einstein condensate in a random potential. Phys. Rev. Lett. 95, 170409 (2005).

    Article  ADS  Google Scholar 

  37. Fort, C. et al. Effect of optical disorder and single defects on the expansion of a Bose–Einstein condensate in a one-dimensional waveguide. Phys. Rev. Lett. 95, 170410 (2005).

    Article  ADS  Google Scholar 

  38. Schulte, T. et al. Routes towards Anderson-like localization of Bose–Einstein condensates in disordered optical lattices. Phys. Rev. Lett. 95, 170411 (2005).

    Article  ADS  Google Scholar 

  39. Clément, D., Bouyer, P., Aspect, A. & Sanchez-Palencia, L. Density modulations in an elongated Bose–Einstein condensate released from a disordered potential. Phys. Rev. A 77, 033631 (2008).

    Article  ADS  Google Scholar 

  40. Chen, Y. P. et al. Phase coherence and superfluid–insulator transition in a disordered Bose–Einstein condensate. Phys. Rev. A 77, 033632 (2008).

    Article  ADS  Google Scholar 

  41. 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 

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

    Article  ADS  Google Scholar 

  43. Basko, D. M., Aleiner, I. L. & Altshuler, B. L. On the problem of many-body localization. Ann. Phys. 321, 1126–1205 (2006).

    Article  ADS  MATH  Google Scholar 

  44. Bilas, N. & Pavloff, N. Anderson localization of elementary excitations in a one dimensional Bose–Einstein condensate. Eur. Phys. J. D 40, 387–397 (2006).

    Article  ADS  Google Scholar 

  45. Lugan, P., Clément, D., Bouyer, P., Aspect, A. & Sanchez-Palencia, L. Anderson localization of Bogolyubov quasiparticles in interacting Bose–Einstein condensates. Phys. Rev. Lett. 99, 180402 (2007).

    Article  ADS  Google Scholar 

  46. Giamarchi, T. & Schulz, H. J. Anderson localization and interactions in one-dimensional metals. Phys. Rev. B 37, 325–340 (1988).

    Article  ADS  Google Scholar 

  47. 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 

  48. Minchau, B. J. & Pelcovits, R. A. Two-dimensional XY model in a random uniaxial field. Phys. Rev. B 32, 3081–3087 (1985).

    Article  ADS  Google Scholar 

  49. Wehr, J., Niederberger, A., Sanchez-Palencia, L. & Lewenstein, M. Disorder versus the Mermin–Wagner–Hohenberg effect: From classical spin systems to ultracold atomic gases. Phys. Rev. B 74, 224448 (2006).

    Article  ADS  Google Scholar 

  50. Niederberger, A. et al. Disorder-induced order in two-component Bose–Einstein condensates. Phys. Rev. Lett. 100, 030403 (2008).

    Article  ADS  Google Scholar 

  51. Mezard, M., Parisi, G. & Virasoro, M. Spin Glass Theory and Beyond (World Scientific, 1987).

    MATH  Google Scholar 

  52. Newman, C. M. & Stein, D. L. Ordering and broken symmetry in short-ranged spin glasses. J. Phys. Condens. Mater 15, R1319–R1364 (2003).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  54. Ahufinger, V., Sanchez-Palencia, L., Kantian, A., Sanpera, A. & Lewenstein, M. Disordered ultracold atomic gases in optical lattices: A case study of Fermi–Bose mixtures. Phys. Rev. A 72, 063616 (2005).

    Article  ADS  Google Scholar 

  55. Mott, N. F. & Twose, W. D. The theory of impurity conduction. Adv. Phys. 10, 107–163 (1961).

    Article  ADS  Google Scholar 

  56. Borland, R. E. The nature of the electronic states in disordered one-dimensional systems. Proc. R. Soc. A 274, 529–545 (1963).

    ADS  MATH  Google Scholar 

  57. Abrahams, E., Anderson, P. W., Licciardello, D. C. & Ramakrishnan, T. V. Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979).

    Article  ADS  Google Scholar 

  58. Ioffe, A. F. & Regel, A. R. Non-crystalline, amorphous and liquid electronic semiconductors. Prog. Semicond. 4, 237–291 (1960).

    Google Scholar 

  59. Mott, N. F. Electrons in disordered structures. Adv. Phys. 16, 49–144 (1967).

    Article  ADS  Google Scholar 

  60. Harper, P. G. Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. A 68, 874–878 (1955).

    Article  ADS  MATH  Google Scholar 

  61. Aubry, S. & André, G. Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Israel Phys. Soc. 3, 133–140 (1980).

    MathSciNet  MATH  Google Scholar 

  62. Lifshits, I. M., Gredeskul, S. A. & Pastur, L. A. Introduction to the Theory of Disordered Systems (Wiley, 1988).

    Google Scholar 

  63. Lugan, P. et al. One-dimensional Anderson localization in certain correlated random potentials. Phys. Rev. A 80, 023605 (2009).

    Article  ADS  Google Scholar 

  64. Gurevich, E. & Kenneth, O. Lyapunov exponent for the laser speckle potential: A weak disorder expansion. Phys. Rev. A 79, 063617 (2009).

    Article  ADS  Google Scholar 

  65. Vollhardt, D. & Wölfle, P. Anderson localization in d≤2 dimensions: A self-consistent diagrammatic theory. Phys. Rev. Lett. 45, 842–845 (1980).

    Article  ADS  Google Scholar 

  66. Kuhn, R. C., Miniatura, C., Delande, D., Sigwarth, O. & Müller, C. A. Localization of matter waves in two-dimensional disordered optical potentials. Phys. Rev. Lett 95, 250403 (2005).

    Article  ADS  Google Scholar 

  67. Shapiro, B. Expansion of a Bose–Einstein condensate in the presence of disorder. Phys. Rev. Lett. 99, 060602 (2007).

    Article  ADS  Google Scholar 

  68. Skipetrov, S. E., Minguzzi, A., van Tiggelen, B. A. & Shapiro, B. Anderson localization of a Bose–Einstein condensate in a 3D random potential. Phys. Rev. Lett. 100, 165301 (2008).

    Article  ADS  Google Scholar 

  69. Anderson, P. W. in Nobel Lectures, Physics 1971–1980 (ed. Lundqvist, S.) (World Scientific, 1992).

    Google Scholar 

  70. Pikovsky, A. S. & Shepelyansky, D. L. Destruction of Anderson localization by a weak nonlinearity. Phys. Rev. Lett. 100, 094101 (2008).

    Article  ADS  Google Scholar 

  71. Kopidakis, G., Komineas, S., Flach, S. & Aubry, S. Absence of wave packet diffusion in disordered nonlinear systems. Phys. Rev. Lett. 100, 084103 (2008).

    Article  ADS  Google Scholar 

  72. Paul, T., Schlagheck, P., Leboeuf, P. & Pavloff, N. Superfluidity versus Anderson localization in a dilute Bose gas. Phys. Rev. Lett. 98, 210602 (2007).

    Article  ADS  Google Scholar 

  73. Lugan, P. et al. Ultracold Bose gases in 1D random potentials: From Lifshits glasses to Bose–Einstein condensates. Phys. Rev. Lett. 98, 170403 (2007).

    Article  ADS  Google Scholar 

  74. Lifshitz, I. M. The energy spectrum of disordered systems. Adv. Phys. 13, 483–536 (1964).

    Article  ADS  MATH  Google Scholar 

  75. Sanchez-Palencia, L. Smoothing effect and delocalization of interacting Bose–Einstein condensates in random potentials. Phys. Rev. A 74, 053625 (2006).

    Article  ADS  Google Scholar 

  76. Falco, G. M., Nattermann, T. V. & Pokrovsky, L. Localized states and interaction-induced delocalization in Bose gases with quenched disorder. Europhys. Lett. 85, 30002 (2009).

    Article  ADS  Google Scholar 

  77. Gurarie, V., Refael, G. & Chalker, J. T. Excitations of the one-dimensional Bose–Einstein condensates in a random potential. Phys. Rev. Lett. 101, 170407 (2008).

    Article  ADS  Google Scholar 

  78. Orso, G. BCS–BEC crossover in a random external potential. Phys. Rev. Lett. 99, 250402 (2007).

    Article  ADS  Google Scholar 

  79. Han, L. & Sa de Melo, C. A. R. Disorder effects during the evolution from BCS to BEC superfluidity. Preprint at <http://arxiv.org/abs/0904.4197> (2009).

  80. Anderson, P. W. Theory of dirty superconductors. J. Phys. Chem. Solids 11, 26–30 (1959).

    Article  ADS  MATH  Google Scholar 

  81. Mott, N. F. Metal–insulator transition. Rev. Mod. Phys. 40, 677–683 (1968).

    Article  ADS  Google Scholar 

  82. Fallani, L., Lye, J. E., Guarrera, V., Fort, C. & Inguscio, M. Ultracold atoms in a disordered crystal of light: Towards a Bose glass. Phys. Rev. Lett. 98, 130404 (2007).

    Article  ADS  Google Scholar 

  83. White, M. et al. Strongly interacting bosons in a disordered optical lattice. Phys. Rev. Lett. 102, 055301 (2009).

    Article  ADS  Google Scholar 

  84. Roscilde, T. Bosons in one-dimensional incommensurate superlattices. Phys. Rev. A 77, 063605 (2008).

    Article  ADS  Google Scholar 

  85. Roux, G. et al. Quasiperiodic Bose–Hubbard model and localization in one-dimensional cold atomic gases. Phys. Rev. A 78, 023628 (2008).

    Article  ADS  Google Scholar 

  86. Delande, D. & Zakrzewski, J. Compression as a tool to detect Bose glass in cold atoms experiments. Phys. Rev. Lett. 102, 085301 (2009).

    Article  ADS  Google Scholar 

  87. Georges, A. in Proc. of the International School of Physics ‘Enrico Fermi’, Course CLXIV (eds Inguscio, M., Ketterle, W. & Salomon, C.) (IOS Press, 2008); preprint at <http://arxiv.org/abs/cond-mat/0702122>.

    Google Scholar 

  88. Byczuk, K., Hofstetter, W. & Vollhardt, D. Competition between Anderson localization and antiferromagnetism in correlated lattice fermion systems with disorder. Phys. Rev. Lett. 102, 146403 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  91. Morrison, S. et al. Physical replicas and the Bose glass in cold atomic gases. New J. Phys. 10, 073032 (2008).

    Article  ADS  Google Scholar 

  92. Paredes, B., Verstraete, F. & Cirac, J. I. Exploiting quantum parallelism to simulate quantum random many-body systems. Phys. Rev. Lett. 95, 140501 (2005).

    Article  ADS  Google Scholar 

  93. Abanin, D. A., Lee, P. A. & Levitov, L. S. Randomness-induced XY ordering in a graphene quantum Hall ferromagnet. Phys. Rev. Lett. 98, 156801 (2007).

    Article  ADS  Google Scholar 

  94. Gavish, U. & Castin, Y. Matter-wave localization in disordered cold atom lattices. Phys. Rev. Lett. 95, 020401 (2005).

    Article  ADS  Google Scholar 

  95. Buonsante, P., Penna, V., Vezzani, A. & Blakie, P. B. Mean-field phase diagram of cold lattice bosons in disordered potentials. Phys. Rev. A 76, 011602 (2007).

    Article  ADS  Google Scholar 

  96. Horstmann, B., Cirac, J. I. & Roscilde, T. Dynamics of localization phenomena for hard-core bosons in optical lattices. Phys. Rev. A 76, 043625 (2007).

    Article  ADS  Google Scholar 

  97. Roscilde, T. & Cirac, J. I. Quantum emulsion: A glassy phase of bosonic mixtures in optical lattices. Phys. Rev. Lett. 98, 190402 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  100. Catani, V., De Sarlo, L., Barontini, G., Minardi, F. & Inguscio, M. Degenerate Bose–Bose mixture in a three-dimensional optical lattice. Phys. Rev. A 77, 011603(R) (2008).

    Article  ADS  Google Scholar 

  101. Lühmann, D.-S., Bongs, K., Sengstock, K. & Pfannkuche, D. Self-trapping of bosons and fermions in optical lattices. Phys. Rev. Lett. 101, 050402 (2008).

    Article  ADS  Google Scholar 

  102. Best, T. et al. Role of interactions in 87Rb–40K Bose–Fermi mixtures in a 3D optical lattice. Phys. Rev. Lett. 102, 030408 (2009).

    Article  ADS  Google Scholar 

  103. Lutchyn, R. M., Tewari, S. & Das Sarma, S. Loss of superfluidity by fermions in the boson Hubbard model on an optical lattice. Phys. Rev. A 79, 011606(R) (2009).

    Article  ADS  Google Scholar 

  104. Dettmer, S. et al. Observation of phase fluctuations in elongated Bose–Einstein condensates. Phys. Rev. Lett. 87, 160406 (2001).

    Article  ADS  Google Scholar 

  105. Richard, S. et al. Momentum spectroscopy of 1D phase fluctuations in Bose–Einstein condensates. Phys. Rev. Lett. 91, 010405 (2003).

    Article  ADS  Google Scholar 

  106. Guerin, W. et al. Guided quasicontinuous atom laser. Phys. Rev. Lett. 97, 200402 (2006).

    Article  ADS  Google Scholar 

  107. Goodman, J. W. Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

    Google Scholar 

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Acknowledgements

This research was supported by the French Centre National de la Recherche Scientifique (CNRS), Agence Nationale de la Recherche (ANR), Triangle de la Physique and Institut Francilien de Recherche sur les Atomes Froids (IFRAF), the German Alexander von Humboldt foundation, the Spanish MEC grants FIS 2005-04627 and Conslider Ingenio 2010 ‘QOIT’, the European Union IP Programme SCALA and the European Science Foundation–MEC Euroquam Project FerMix.

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  1. Laboratoire Charles Fabry de l’Institut d’Optique, CNRS and Univ. Paris-Sud, Campus Polytechnique, RD 128, F-91127 Palaiseau cedex, France

    Laurent Sanchez-Palencia

  2. ICREA—Institució Catalana de Recerca i Estudis Avançats and ICFO—Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, E-08860 Castelldefels, Barcelona

    Maciej Lewenstein

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Sanchez-Palencia, L., Lewenstein, M. Disordered quantum gases under control. Nature Phys 6, 87–95 (2010). https://doi.org/10.1038/nphys1507

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