Spin-orbit-coupled Bose-Einstein condensate in a tilted optical lattice

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 4, 2010, Pages

  Larson, Jonas ^a,b   Martikainen, Jani Petri ^a   Collin, Anssi ^a   Sjöqvist, Erik ^c,d  

^a NORDITA   (Denmark)

^b STOCKHOLM UNIVERSITY   (Sweden)

^c UPPSALA UNIVERSITY   (Sweden)

^d NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

BLOCH OSCILLATIONS; BOSE-EINSTEIN CONDENSATES; IN-PHASE; INTRINSIC SPIN; LIGHT FIELDS; OPTICAL LATTICES; OPTICAL-LATTICE POTENTIAL; PERIODIC POTENTIALS; SPIN ORBITS; SPIN-ORBIT COUPLINGS; STRONG CORRELATION; TRANSVERSE SPIN CURRENTS; ULTRACOLD ATOMS;

CRYSTAL LATTICES; HALL EFFECT; OPTICAL MATERIALS; SEMICONDUCTING INDIUM GALLIUM ARSENIDE; SOLID STATE PHYSICS; STATISTICAL MECHANICS; STEAM CONDENSERS;

MAGNETIC FIELD EFFECTS;

EID: 78650930996     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.043620     Document Type: Article

References (104)

1. I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.323 76, 323 (2004). (Pubitemid 39063520)
2. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science SCIEAS 0036-8075 10.1126/science.1065389 294, 1488 (2001). (Pubitemid 33063913)
3. M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.083901 93, 083901 (2004);
4. K. Yu. Bliokh and Yu. P. Bliokh, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.026605 70, 026605 (2004);
5. K. Yu. Bliokh and Yu. P. Bliokh, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.10.035 333, 181 (2004);
6. K. Yu. Bliokh and Yu. P. Bliokh, Nat. Photonics PYLAAG 1749-4885 10.1038/nphoton.2008.229 2, 748 (2008);
7. O. Hosten and P. G. Kwiat, Science SCIEAS 0036-8075 10.1126/science. 1152697 319, 787 (2008). (Pubitemid 351225863)
8. A. M. Dudarev, R. B. Diener, I. Carusotto, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.153005 92, 153005 (2004);
9. X.-J. Liu, X. Liu, L. C. Kwek, and C. H. Oh, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.026602 98, 026602 (2007); (Pubitemid 46135158)
10. J. Y. Vaishnav, J. Ruseckas, C. W. Clark, and G. Juzelunas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.265302 101, 265302 (2008);
11. X.-J. Liu, M. F. Borunda, X. Liu, and J. Sinova, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.046402 102, 046402 (2009).
12. M. Taillefumier, E. K. Dahl, A. Brataas, and W. Hofstetter, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.80.020407 80, 020407 (R) (2009).
13. Y. A. Bychkov and E. I. Rashba, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/33/015 17, 6039 (1984).
14. G. Dresselhaus, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.100.580 100, 580 (1955).
15. J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.126603 92, 126603 (2004).
16. T. Jungwirth, Q. Niu, and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.207208 88, 207208 (2002).
17. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.82.1539 82, 1539 (2010);
18. Y. Tian, L. Ye, and X. Jin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.087206 103, 087206 (2009).
19. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730701223200 56, 243 (2007). (Pubitemid 46710973)
20. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.885 80, 885 (2008).
21. M. H. Anderson, J. R. Enscher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science SCIEAS 0036-8075 10.1126/science.269.5221.198 269, 198 (1995);
22. K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.3969 75, 3969 (1995).
23. C. J. Pethick and H. Smith, Bose-Einsten Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2008).
24. C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.586 78, 586 (1997);
25. J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, Nature (London) NATUAS 0028-0836 10.1038/24567 396, 345 (1998); (Pubitemid 28557389)
26. D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, S. Inouye, J. Stenger, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 83.661 83, 661 (1999);
27. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.010407 91, 010407 (2003);
28. L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalottore, and M. S. Stamper-Kurn, Nature (London) NATUAS 0028-0836 10.1038/nature05094 443, 312 (2006); (Pubitemid 44435146)
29. J. Larson and J.-P. Martikainen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.033605 80, 033605 (2009).
30. R. Dum and M. Olshanii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1788 76, 1788 (1996).
31. J. Ruseckas, G. Juzeliunas, P. Öhberg, and M. Fleischhauer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010404 95, 010404 (2005). (Pubitemid 41506411)
32. S. K. Dutta, B. K. Teo, and G. Raithel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1934 83, 1934 (1999).
33. 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);
34. Y.-J. Lin, R. L. Compton, K. Jiménez-Garcia, J. V. Porto, and I. B. Spielman, Nature (London) NATUAS 0028-0836 10.1038/nature08609 462, 628 (2009).
35. T. D. Stanescu, C. Zhang, and V. Galitski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.110403 99, 110403 (2007). (Pubitemid 47429423)
36. J. Larson and E. Sjöqvist, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.043627 79, 043627 (2009).
37. B. Thaller, The Dirac Equation (Springer Verlag, Berlin, 1992).
38. R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, Nature (London) NATUAS 0028-0836 10.1038/nature08688 463, 68 (2010).
39. It is worth pointing out that even if a confining trap is absent in the actual BO experiments, it is present during the condensation process and as it is turned off before releasing the condensate in the tilted lattice it implies, in the local density approximation, that the chemical potential varies within the extent of the atomic cloud which renders a source for decoherence (see [25])
40. O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.140402 87, 140402 (2001); (Pubitemid 32962123)
41. M. Cristiani, O. Morsch, J. H. Müller, D. Ciampini, and E. Arimondo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.063612 65, 063612 (2002);
42. J. H. Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/35/14/307 35, 3095 (2002); (Pubitemid 34854562)
43. M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100. 080404 100, 080404 (2008). (Pubitemid 351419060)
44. J. Y. Vaishnav and C. W. Clark, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.153002 100, 153002 (2008). (Pubitemid 351555261)
45. F. Mireles and G. Kirczenow, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.64.024426 64, 024426 (2001);
46. L. W. Molenkamp, G. Schmidt, and G. E. W. Bauer, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.64.121202 64, 121202 (2001).
47. A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, and T. E. Tiwald, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.62.7365 62, 7365 (2000). (Pubitemid 32323635)
48. T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.69.1757 69, 1757 (2000);
49. C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 95, 226801 (2005); (Pubitemid 41776999)
50. H. Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, L. Kleinman, and A. H. MacDonald, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.74.165310 74, 165310 (2006). (Pubitemid 44537122)
51. S. Y. Zhou, G.-H. Gweon, J. Graf, A. F. Federov, C. D. Spataru, R. D. Diehl, Y. Kopelevich, D.-H. Lee, S. G. Louie, and A. Lanzara, Nat. Phys. PRLTAO 1745-2473 10.1038/nphys393 2, 595 (2006). (Pubitemid 44328344)
52. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature (London) NATUAS 0028-0836 10.1038/nature04233 438, 197 (2005). (Pubitemid 41599867)
53. T.-L. Ho and S. Zhang, e-print arXiv: 1007.0650.
54. M. BenDahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.4508 76, 4508 (1996).
55. C. A. Mead and D. G. Truhlar, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.437734 70, 2284 (1979);
56. C. A. Mead, Chem. Phys. CMPHC2 0301-0104 10.1016/0301-0104(80)85035-X 49, 23 (1980);
57. C. A. Mead, Chem. Phys. CMPHC2 0301-0104 10.1016/0301-0104(80)85036-1 49, 33 (1980);
58. C. A. Mead, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.64.51 64, 51 (1992).
59. M. V. Berry, Proc. R. Soc. London A RMPHAT 1364-5021 10.1098/rspa.1984. 0023 392, 45 (1984).
60. F. Wilczek and A. Zee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.2111 52, 2111 (1984).
61. R. G. Unanyan, B. W. Shore, and K. Bergmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.2910 59, 2910 (1999).
62. G. Juzeliunas, J. Ruseckas, A. Jacob, L. Santos, and P. Öhberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.200405 100, 200405 (2008). (Pubitemid 351725972)
63. J.-M. Hou, W.-X. Yang, and X.-J. Liu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.043621 79, 043621 (2009).
64. S.-L. Zhu, H. Fu, C.-J. Wu, S.-C. Zhang, and L.-M. Duan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.240401 97, 240401 (2006). (Pubitemid 44907661)
65. T. D. Stanescu, B. Anderson, and V. Galitski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.023616 78, 023616 (2008).
66. V. Pietilä and M. Möttönen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.080403 102, 080403 (2009).
67. J. Larson and S. Stenholm, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.033805 73, 033805 (2006). (Pubitemid 43334249)
68. A. Jacob, P. Öhberg, G. Juzeliunas, and L. Santos, Appl. Phys. B APBOEM 0946-2171 10.1007/s00340-007-2865-6 89, 439 (2007). (Pubitemid 50005540)
69. G. Juzeliunas, J. Ruseckas, M. Lindberg, L. Santos, and P. Öhberg, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.011802 77, 011802 (R) (2008). (Pubitemid 351178661)
70. S. K. Wong, Nuovo Cimento A NCIAAT 0369-3546 10.1007/BF02892134 65, 689 (1970).
71. B. K. Nikolic, L. P. Zarbo, and S. Welack, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.72.075335 72, 075335 (2005). (Pubitemid 41506514)
72. V. Y. Demikhovskii and D. V. Khmisky, J. Exp. Theor. Phys. JTPLA2 0021-3640 10.1134/S0021364006080091 83, 340 (2006); (Pubitemid 43954157)
73. S. Smirnov, D. Bercioux, and M. Grifoni, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/80/27003 80, 27003 (2007);
74. D. V. Khmiisky, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.205401 79, 205401 (2009).
75. H. C. Longuet-Higgins, U. Opik, M. H. L. Pryce, and R. A. Sack, Proc. R. Soc. A EULEEJ 1364-5021 10.1098/rspa.1958.0022 244, 1 (1958);
76. D. R. Yarkony, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.68.985 68, 985 (1996).
77. R. Shen, L. B. Shao, B. Wang, and D. Y. Xing, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.81.041410 81, 041410 (R) (2010).
78. V. Grecchi and A. Sacchetti, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.63.212303 63, 212303 (2001).
79. F. Bloch, Z. Phys. 52, 555 (1928);
80. D. I. Choi and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.2022 82, 2022 (1999).
81. K. Leo, P. H. Bolivar, F. Bruggemann, R. Schwedler, and K. Kohler, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(92)90798-E 84, 943 (1992); (Pubitemid 23620476)
82. J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, Phys. Rev. B SSCOA4 1098-0121 10.1103/PhysRevB.46.7252 46, 7252 (1992).
83. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.4756 83, 4756 (1999);
84. T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.4752 83, 4752 (1999).
85. H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.053903 96, 053903 (2006). (Pubitemid 43270952)
86. L. D. Landau, Phys. Z. USSR 2, 46 (1932);
87. C. Zener, Proc. R. Soc. London A PRLTAO 1364-5021 10.1098/rspa.1932.0165 137, 696 (1932).
88. M. Holthaus, J. Phys. B JOBOFD 1464-4266 10.1088/1464-4266/2/5/306 2, 589 (2000). (Pubitemid 32027714)
89. M. Baer, Beyond Born-Oppenheimer (Wiley, New York, 2006).
90. D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.4531 81, 4531 (1998).
91. J. Larson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.051803 81, 051803 (R) (2010).
92. M. D. Flei, J. A. Fleck, and A. Steiger, J. Comput. Phys. JCTPAH 0021-9991 10.1016/0021-9991(82)90091-2 47, 412 (1982).
93. B. Wu and Q. Niu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61. 023402 61, 023402 (2000);
94. J. Liu, B. Wu, and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.170404 90, 170404 (2003);
95. M. Machholm, C. J. Pethick, and H. Smith, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.053613 67, 053613 (2003).
96. J. Liu, L. Fu, B.-Y. Ou, S.-G. Chen, D. I. Choi, B. Wu, and Q. Niu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.023404 66, 023404 (2002).
97. T. Gericke, P. Würtz, D. Reitz, T. Langen, and H. Ott, Nat. Phys. PLRAAN 1745-2473 10.1038/nphys1102 4, 949 (2008);
98. N. Gemelke, X. Zhang, Ch.-L. Hung, and Ch. Chin, Nature (London) NATUAS 0028-0836 10.1038/nature08244 460, 995 (2009);
99. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, Nature (London) NATUAS 0028-0836 10.1038/nature08482 462, 74 (2009);
100. J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, Nature (London) 0028-0836 10.1038/nature09378 467, 68 (2010).
101. K. J. Gunter, M. Cheneau, T. Yefsah, S. P. Rath, and J. Dalibard, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.011604 79, 011604 (2009).
102. W. V. Liu and C. Wu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74. 013607 74, 013607 (2006). (Pubitemid 44464306)
103. 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).
104. Q. Zhang, J. Gong, and C. H. Oh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.023608 81, 023608 (2010).