Exploring the grand-canonical phase diagram of interacting bosons in optical lattices by trap squeezing

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 2, 2010, Pages

  Roscilde, Tommaso ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BAND INSULATORS; BOSE GLASS; BOSE HUBBARD MODEL; BOSON MODELS; CENTRAL DENSITY; COHERENCE PROPERTIES; EXPERIMENTAL PARAMETERS; HAMILTONIAN PARAMETERS; HIGH DENSITY; INTERACTING BOSONS; MEAN-FIELD; MOTT INSULATORS; ONE DIMENSIONAL OPTICAL LATTICE; OPTICAL LATTICES; PARABOLIC TRAP; PARAMETER RANGE; QUANTUM FLUCTUATION; QUANTUM MONTE CARLO; QUANTUM SIMULATORS; SCALING BEHAVIOR; SCALING RELATIONS; THOMAS-FERMI; TIME OF FLIGHT MEASUREMENTS; TRAP CENTER; TRAPPING POTENTIAL; WEAK INTERACTIONS;

BIOELECTRIC PHENOMENA; CHEMICAL POTENTIAL; CHEMICALS; COMPRESSIBILITY; CRYSTAL LATTICES; HAMILTONIANS; HUBBARD MODEL; OPTICAL MATERIALS; PHASE DIAGRAMS; PHYSICAL OPTICS; QUANTUM ELECTRONICS;

BOSONS;

EID: 77955794755     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.023601     Document Type: Article

References (75)

1. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.885 80, 885 (2008).
2. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen (De), and U. Sen, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730701223200 56, 243 (2007). (Pubitemid 46710973)
3. R. P. Feynman, Int. J. Theor. Phys. IJTPBM 0020-7748 10.1007/BF02650179 21, 467 (1982).
4. R. B. Diener, Q. Zhou, H. Zhai, and T.-L. Ho, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.180404 98, 180404 (2007). (Pubitemid 46701732)
5. T.-L. Ho and Q. Zhou, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.120404 99, 120404 (2007). (Pubitemid 47443740)
6. B. Capogrosso-Sansone, E. Kozik, N. Prokofev, and B. Svistunov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.013619 75, 013619 (2007). (Pubitemid 46130348)
7. L. Pollet, C. Kollath, K. Van Houcke, and M. Troyer, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/6/065001 10, 065001 (2008).
8. D. M. Weld, P. Medley, H. Miyake, D. Hucul, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.245301 103, 245301 (2009).
9. D. McKay, M. White, and B. DeMarco, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.063605 79, 063605 (2009).
10. D. McKay and B. DeMarco, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/5/055013 12, 055013 (2010).
11. Q. Zhou and T.-L. Ho, e-print arXiv: 0908.3015.
12. S. Trotzky, L. Pollet, F. Gerbier, U. Schnorrberger, I. Bloch, N. V. Prokof'ev, B. Svistunov, and M. Troyer, e-print arXiv: 0905.4882.
13. R. Joerdens, L. Tarruell, D. Greif, T. Uehlinger, N. Strohmaier, H. Moritz, T. Esslinger, L. De Leo, C. Kollath, A. Georges, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.180401 104, 180401 (2010).
14. G. Murthy, D. P. Arovas, and A. Auerbach, Phys. Rev. B IJTPBM 1098-0121 10.1103/PhysRevB.55.3104 55, 3104 (1997).
15. M. Boninsegni, J. Low Temp. Phys. JLTPAC 0022-2291 10.1023/A: 1023741108312 132, 39 (2003). (Pubitemid 36854887)
16. P. Sengupta, L. P. Pryadko, F. Alet, M. Troyer, and G. Schmid, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.207202 94, 207202 (2005). (Pubitemid 41481108)
17. V. W. Scarola, E. Demler, and S. Das Sarma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.051601 73, 051601 (2006).
18. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.40.546 40, 546 (1989).
19. Q. Zhou, Y. Kato, N. Kawashima, and N. Trivedi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.085701 103, 085701 (2009).
20. T.-L. Ho and Q. Zhou, Nature Phys. PRLTAO 1745-2473 10.1038/nphys1477 6, 131 (2009).
21. T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.130403 92, 130403 (2004).
22. L. Fallani, J. E. Lye, V. Guarrera, C. Fort, and M. Inguscio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.130404 98, 130404 (2007). (Pubitemid 46515826)
23. D. Clément, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.155301 102, 155301 (2009).
24. P. T. Ernst, S. Götze, J. S. Krauser, K. Pyka, D.-S. Lühmann, D. Pfannkuche, and K. Sengstock, Nature Phys. PRLTAO 1745-2473 10.1038/nphys1476 6, 56 (2009).
25. K. D. Nelson, X. Li, and D. S. Weiss, Nature Phys. PRLTAO 1745-2473 10.1038/nphys645 3, 556 (2007).
26. T. Gericke, P. Würtz, D. Reitz, T. Langen, and H. Ott, Nature Phys. PRLTAO 1745-2473 10.1038/nphys1102 4, 949 (2008).
27. N. Gemelke, X. Zhang, C.-L. Hung, and C. Chin, Nature NATUAS 0028-0836 10.1038/nature08244 460, 995 (2009).
28. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, Nature NATUAS 0028-0836 10.1038/nature08482 462, 74 (2009).
29. J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, e-print arXiv: 1006.3799 (2010).
30. T. Roscilde, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/11/2/023019 11, 023019 (2009).
31. U. Schneider, L. Hackermuller, S. Will, T. Best, I. Bloch, T. A. Costi, R. W. Helmes, D. Rasch, and A. Rosch, Science SCIEAS 0036-8075 10.1126/science.1165449 322, 1520 (2008).
32. S. Fölling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. Müller, and I. Bloch, Nature NATUAS 0028-0836 10.1038/nature06112 448, 1029 (2007). (Pubitemid 47345592)
33. M. Anderlini, Nature NATUAS 0028-0836 10.1038/nature06011 448, 452 (2007). (Pubitemid 47123519)
34. S. Bergkvist, P. Henelius, and A. Rosengren, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.053601 70, 053601 (2004). (Pubitemid 40072990)
35. S. Wessel, F. Alet, M. Troyer, and G. G. Batrouni, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.053615 70, 053615 (2004). (Pubitemid 40079096)
36. T. Roscilde, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.063605 77, 063605 (2008).
37. Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.013406 75, 013406 (2007). (Pubitemid 46130341)
38. C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, UK, 2002).
39. A. W. Sandvik, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.59.R14157 59, R14157 (1999);
40. O. F. Syljuåsen, Phys. Rev. E PLRAAN 1539-3755 10.1103/PhysRevE.67. 046701 67, 046701 (2003).
41. M. Rizzi, D. Rossini, G. De Chiara, S. Montangero, and R. Fazio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.240404 95, 240404 (2005). (Pubitemid 43272912)
42. M. Rigol, A. Muramatsu, G. G. Batrouni, and R. T. Scalettar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.130403 91, 130403 (2003).
43. M. Rigol and A. Muramatsu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.053612 69, 053612 (2004);
44. M. Rigol and A. Muramatsu, Opt. Commun. OPCOB8 0030-4018 10.1016/j.optcom.2004.10.040 243, 33 (2004).
45. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(61)90115-4 16, 407 (1961).
46. L. Fallani and C. Fort (private communication).
47. B. Capogrosso-Sansone, S. G. Soyler, N. Prokofev, and B. Svistunov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.015602 77, 015602 (2008). (Pubitemid 351197996)
48. B. Capogrosso-Sansone, N. V. Prokof'ev, and B. V. Svistunov, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.75.134302 75, 134302 (2007).
49. We notice that the μ data for the d = 3 system in a superlattice are much more scattered than for all the other cases, as shown on the right panel of Fig. 7. This is due to strong size effects on the system considered, which are inevitable in d = 3 due to the short linear size of each spatial dimension. (We have considered cubes with up to L = 18 sites on each side, but the particles are actually confined on a region with even smaller linear extent.) In the presence of a superlattice potential, a system on such a finite size experiences only a few wells of the potential in each spatial dimension, and hence the nonlinearities due to such potential become relevant and cannot be simply averaged out as in the TF/AL approach.
50. G. G. Batrouni, H. R. Krishnamurthy, K. W. Mahmud, V. G. Rousseau, and R. T. Scalettar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.023627 78, 023627 (2008).
51. M. Rigol, G. G. Batrouni, V. G. Rousseau, and R. T. Scalettar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.053605 79, 053605 (2009).
52. R. Jördens, N. Strohmaier, K. Günter, H. Moritz, and T. Esslinger, Nature NATUAS 0028-0836 10.1038/nature07244 455, 204 (2008).
53. V. W. Scarola, L. Pollet, J. Oitmaa, and M. Troyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.135302 102, 135302 (2009).
54. T. Kinoshita, T. Wenger, and D. S. Weiss, Nature NATUAS 0028-0836 10.1038/nature04693 440, 900 (2006).
55. M. Greiner, O. Mandel, T. W. Hänsch, and I. Bloch, Nature NATUAS 0028-0836 10.1038/nature00968 419, 51 (2002). (Pubitemid 34987866)
56. J. Dziarmaga, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 245701 95, 245701 (2005). (Pubitemid 43272890)
57. G. Pupillo, A. M. Rey, C. J. Williams, and C. W. Clark, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/8/161 8, 161 (2006). (Pubitemid 44385052)
58. - 4 J and whose smallness might be limited by the resolution of the grid with which we sample the trapping strength.
59. A. Aubry and C. André, in Proceedings of the Israel Physical Society, edited by, C. G. Kuper III, (Adam Hilger, Bristol, UK, 1979).
60. J. B. Sokoloff, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(85)90088-2 126, 189 (1985).
61. I. B. Spielman, W. D. Phillips, and J. V. Porto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.080404 98, 080404 (2007). (Pubitemid 46326138)
62. D. J. Han, M. T. DePue, and D. S. Weiss, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.023405 63, 023405 (2001).
63. W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.2253 70, 2253 (1993).
64. C.-S. Chuu, F. Schreck, T. P. Meyrath, J. L. Hanssen, G. N. Price, and M. G. Raizen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.260403 95, 260403 (2005). (Pubitemid 43061514)
65. Y. Shin, C. H. Schunck, A. Schirotzek, and W. Ketterle, Nature NATUAS 0028-0836 10.1038/nature06473 451, 689 (2008). (Pubitemid 351222591)
66. Y.-A. Liao, A. S. C. Rittner, T. Paprotta, W. Li, G. B. Partridge, R. G. Hulet, S. K. Baur, and E. J. Mueller, e-print arXiv: 0912.0092.
67. The standard definition of the lattice momentum distribution would involve a normalization to the volume L d of the quantization box, but in the case of a trapped system, the quantization box is arbitrary. As an alternative, here we imagine that the quantization box is fixed to the number of bosons N, which is a convenient convention, given that this number is kept fixed in our study of a trapped system. In this case, the condensate occupation n (k = 0) takes the meaning of the number of particles with momenta in the box k ≤ π / (a N), where a is the lattice spacing.
68. Reference [49] has documented that local-density signatures of the onset of the Mott phase in a trap show up at a higher U / J value than in the bulk for one- and two-dimensional systems and that this blue shift is much more pronounced for higher trapping potentials V t. A similar shift has been experimentally documented in K. Jiménez-García, R. L. Compton, Y.-J. Lin, W. D. Phillips, J. V. Porto, and I. B. Spielman, e-print arXiv: 1003.1541, based on time-of-flight measurements of bosons trapped in quasi-two-dimensional optical lattices. We find that these observations are fully consistent with our observations for the central compressibility (Fig. 16) and for the time-of-flight observables (Fig. 19) of a one-dimensional system and that they can be easily explained with the fact that the onset of an MI phase with a small gap Δ is hindered by the trap inhomogeneity: Indeed, the trapping potential discards the MI behavior beyond a length scale r i - r 0 from the trap center, such that V t (r i - r 0) 2 Δ.
69. G. Roux, T. Barthel, I. P. McCulloch, C. Kollath, U. Schollwock, and T. Giamarchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.023628 78, 023628 (2008).
70. X. Deng, R. Citro, A. Minguzzi, and E. Orignac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.013625 78, 013625 (2008).
71. D. Delande and J. Zakrzewski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.085301 102, 085301 (2009).
72. i is actually the column-integrated density of a three-dimensional system, but this aspect is actually irrelevant for our discussion.
73. We avoid extracting the central and global compressibilities by differentiating the related densities, because of the significant numerical noise associated with the derivative. Nonetheless, the changes in slope in Fig. 25 are evident.
74. W. Zwerger, J. Opt. B 5, S9 (2003).
75. y) = N, which is not satisfied in turn by the formula of Paredes (Pubitemid 38684809)