Effects of smooth boundaries on topological edge modes in optical lattices

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 85, Issue 6, 2012, Pages

  Buchhold, Michael ^a   Cocks, Daniel ^a   Hofstetter, Walter ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC CLOUDS; BRAGG SPECTROSCOPY; DETECTION METHODS; EDGE STATE; GAUGE FIELDS; NEUTRAL ATOMS; OPTICAL LATTICES; QUANTUM HALL; QUANTUM NUMBERS; QUANTUM SPIN HALLS; SHARP BOUNDARIES; SMOOTH BOUNDARY; SOLID-STATE SYSTEM; SPATIALLY RESOLVED; SPLITTING AND MERGING; ULTRACOLD ATOMS;

ATOMS; BRAGG CELLS; OPTICAL MATERIALS; QUANTUM CONFINEMENT; TOPOLOGY;

CRYSTAL LATTICES;

EID: 84862673590     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.85.063614     Document Type: Article

References (63)

1. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.885 80, 885 (2008).
2. N. R. Cooper, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730802564122 57, 539 (2008).
3. Y.-J. Lin, R. L. Compton, A. R. Perry, W. D. Phillips, J. V. Porto, and I. B. Spielman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.130401 102, 130401 (2009).
4. Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, and I. B. Spielman, Nature (London) NATUAS 0028-0836 10.1038/nature08609 462, 628 (2009).
5. 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)
6. N. R. Cooper, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.106.175301 106, 175301 (2011).
7. D. Jaksch and P. Zoller, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/5/1/356 5, 56 (2003).
8. E. J. Mueller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.041603 70, 041603 (R) (2004).
9. A. S. Sorensen, E. Demler, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.086803 94, 086803 (2005). (Pubitemid 40620676)
10. I. B. Spielman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.063613 79, 063613 (2009).
11. F. Gerbier and J. Dalibard, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/3/033007 12, 033007 (2010).
12. K. Jiménez-García, L. J. LeBlanc, R. A. Williams, M. C. Beeler, A. R. Perry, and I. B. Spielman, arXiv: 1201.6630.
13. J. Dalibard, F. Gerbier, G. Juzeliũnas, and P. Öhberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.83.1523 83, 1523 (2011).
14. L.-K. Lim, A. Hemmerich, and C. M. Smith, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.023404 81, 023404 (2010).
15. Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, Nature NATUAS 0028-0836 10.1038/nature09887 471, 83 (2011).
16. N. Goldman, W. Beugeling, and C. M. Smith, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/97/23003 97, 23003 (2012).
17. K. Osterloh, M. Baig, L. Santos, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010403 95, 010403 (2005). (Pubitemid 41506410)
18. J. Ruseckas, G. Juzeliũnas, P. Öhberg, and M. Fleischhauer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010404 95, 010404 (2005). (Pubitemid 41506411)
19. M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y. A. Chen, and I. Bloch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.255301 107, 255301 (2011).
20. J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.108.225304 108, 225304 (2012).
21. T. D. Stanescu, V. Galitski, J. Y. Vaishnav, C. W. Clark, and S. Das Sarma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.053639 79, 053639 (2009).
22. T. D. Stanescu, V. Galitski, and S. Das Sarma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.013608 82, 013608 (2010).
23. N. Goldman, I. Satija, P. Nikolic, A. Bermudez, M. A. Martin-Delgado, M. Lewenstein, and I. B. Spielman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.255302 105, 255302 (2010).
24. D. R. Hofstadter, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.14.2239 14, 2239 (1976).
25. Y. Hatsugai, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.48.11851 48, 11851 (1993).
26. K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.45.494 45, 494 (1980).
27. F. Delahaye, D. Dominguez, Y. Guldner, J. P. Hirtz, M. Razeghi, J. P. Vieren, and J. P. Voos, Phys. Rev. B 1098-0121 10.1103/PhysRevB.33.3990 33, 3990 (1986).
28. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-c. Zhang, Science SCIEAS 0036-8075 10.1126/science.1148047 318, 766 (2007). (Pubitemid 351411764)
29. C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 95, 146802 (2005). (Pubitemid 41777602)
30. B. A. Bernevig and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.106802 96, 106802 (2006).
31. M. Kohmoto, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.39.11943 39, 11943 (1989).
32. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.82.3045 82, 3045 (2010).
33. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.49.405 49, 405 (1982).
34. Y. Hatsugai, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/9/12/003 9, 2507 (1997).
35. A. M. Essin and V. Gurarie, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.125132 84, 125132 (2011).
36. y being chosen on a 100 points grid in the interval [- π / a, π / a].
37. y is a well defined quantum number.
38. C. Wu, B. A. Bernevig, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.106401 96, 106401 (2006).
39. C. Xu and J. E. Moore, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73. 045322 73, 045322 (2006). (Pubitemid 43270648)
40. y, ω).
41. O. Gygi, H. G. Katzgraber, M. Troyer, S. Wessel, and G. G. Batrouni, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.063606 73, 063606 (2006). (Pubitemid 44050336)
42. S. Will, T. Best, U. Schneider, L. Hackermüller, D.-S. Lühmann, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/nature09036 465, 197 (2010).
43. S. Will, T. Best, S. Braun, U. Schneider, and I. Bloch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.115305 106, 115305 (2011).
44. 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)
45. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature NATUAS 0028-0836 10.1038/nature07000 453, 891 (2008). (Pubitemid 351832566)
46. L. Sanchez-Palencia and M. Lewenstein, Nat. Phys. 1745-2473 10.1038/nphys1507 6, 87 (2010).
47. y), where ψ (x, y) is the single-particle wave function).
48. At this point, one has to keep in mind that we are investigating the properties of a finite system, which has per construction only localized eigenstates. Localization or delocalization therefore means confinement to few lattice sites or an extension over various sites and must be understood from the context.
49. D. Makogon, I. B. Spielman, and C. Morais-Smith, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/97/33002 97, 33002 (2012).
50. N. Goldman, I. Satija, P. Nikolic, A. Bermudez, M. A. Martin-Delgado, M. Lewenstein, and I. B. Spielman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett. 105.255302 105, 255302 (2010).
51. A. Messiah, Quantum Mechanics, Vol. I (Wiley, New York, 1961).
52. C. Cohen-Tannoudji, B. Diu, and F. Lalöe, Quantum Mechanics (Wiley, New York, 1977).
53. V. W. Scarola and S. Das Sarma, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.98.210403 98, 210403 (2007). (Pubitemid 47139692)
54. X.-J. Liu, X. Liu, C. Wu, and J. Sinova, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.033622 81, 033622 (2010).
55. N. Goldman, J. Beugnon, and F. Gerbier, arXiv: 1203.1246v1.
56. T.-L. Dao, A. Georges, J. Dalibard, C. Salomon, and I. Carusotto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.240402 98, 240402 (2007). (Pubitemid 47139861)
57. R. O. Umucalilar, H. Zhai, and M. O. Oktel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.070402 100, 070402 (2008). (Pubitemid 351393606)
58. E. Zhao, N. Bray-Ali, C. J. Williams, I. B. Spielman, and I. I. Satija, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.84.063629 84, 063629 (2011).
59. E. Alba, X. Fernandez-Gonzalvo, J. Mur-Petit, J. K. Pachos, and J. J. Garcia-Ripoll, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.107.235301 107, 235301 (2011).
60. D. M. Stamper-Kurn, A. P. Chikkatur, A. Gorlitz, S. Inouye, S. Gupta, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2876 83, 2876 (1999).
61. J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.4569 82, 4569 (1999).
62. J. Steinhauer, R. Ozeri, N. Katz, and N. Davidson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.120407 88, 120407 (2002).
63. J. W. Negele and H. Orland, Quantum Many-Particle Systems (Addison-Wesley, Redwood City, CA, 1988).