Please wait a minute...
Shopping Cart Email List Chinese
Advanced Search Fig/Tab
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Featured Articles  |  Most Downloaded  |  Most Reading
Online Submission Subscribe to Our RSS Content Feed
Front. Phys.    2012, Vol. 7 Issue (1) : 31-53    https://doi.org/10.1007/s11467-011-0223-y
REVIEW ARTICLE
Relativistic quantum effects of Dirac particles simulated by ultracold atoms
Dan-wei Zhang (张丹伟)1,2, Zi-dan Wang (汪子丹)2, Shi-liang Zhu (朱诗亮)1()
1. Laboratory of Quantum Information Technology, School of Physics & Telecommunication Engineering, South China Normal University, Guangzhou 510006, China; 2. Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
 Download: PDF(810 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.
Keywords ultracold atoms      Dirac equation      quantum simulation     
Corresponding Author(s): Shi-liang Zhu (朱诗亮),Email:slzhu@scnu.edu.cn   
Issue Date: 01 February 2012
 Cite this article:   
Dan-wei Zhang (张丹伟),Zi-dan Wang (汪子丹),Shi-liang Zhu (朱诗亮). Relativistic quantum effects of Dirac particles simulated by ultracold atoms[J]. Front. Phys. , 2012, 7(1): 31-53.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-011-0223-y
https://academic.hep.com.cn/fop/EN/Y2012/V7/I1/31
1 R. Feynman, Int. J. Theor. Phys. , 1982, 21(6-7): 467
2 See the reviews in Insight: Quantum Coherence, Nature , 2008, 453(7198): 1003
3 I. Buluta and F. Nori, Science , 2009, 326(5949): 108
4 M. Greiner, O. Mandel, T. Esslinger, T. W. H?nsch, and I. Bloch, Nature , 2002, 415(6867): 39
5 T. St?ferle, H. Moritz, C. Schori, M. K?hl, and T. Esslinger, Phys. Rev. Lett. , 2004, 92(13): 130403
6 I. B. Spielman, W. D. Phillips, and J. V. Porto, Phys. Rev. Lett. , 2007, 98(8): 080404
7 J. Simon, W. S. Bakr, R. Ma, M. E. Tai, P. M. Preiss, and M. Greiner, Nature , 2011, 472(7343): 307
8 A. Friedenauer, H. Schmitz, J. T. Glueckert, D. Porras, and T. Schaetz, Nat. Phys. , 2008, 4(10): 757
9 K. Kim, M. S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G. D. Lin, L. M. Duan, and C. Monroe, Nature , 2010, 465(7298): 590
10 R. Gerritsma, G. Kirchmair, F. Z?hringer, E. Solano, R. Blatt, and C. F. Roos, Nature , 2010, 463(7277): 68
11 R. Gerritsma, B. P. Lanyon, G. Kirchmair, F. Z?hringer, C. Hempel, J. Casanova, J. J. Garcá-Ripoll, E. Solano, R. Blatt, and C. F. Roos, Phys. Rev. Lett. , 2011, 106(6): 060503
12 J. T. Barreiro, M. M¨uler, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, and R. Blatt, Nature , 2011, 470(7335): 486
13 J. Du, N. Xu, X. Peng, P. Wang, S. Wu, and D. Lu, Phys. Rev. Lett. , 2010, 104(3): 030502
14 M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science , 1995, 269(5221): 198
15 F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. , 1999, 71(3): 463
16 C. A. Regal, M. Greiner, and D. S. Jin, Phys. Rev. Lett. , 2004, 92(4): 040403
17 S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. , 2008, 80(4): 1215
18 J. Liu and B. Liu, Front. Phys. China , 2010, 5(2): 123
19 H. Jing, Y. Jiang, and Y. Deng, Front. Phys. , 2011, 6(1): 15
20 M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sende, and U. Sen, Adv. Phys. , 2007, 56(2): 243
21 H. Zhai, Front. Phys. China , 2009, 4(1): 1
22 A. Klein and D. Jaksch, Phys. Rev. A , 2006, 73(5): 053613
23 M. A. Baranov, K. Osterloh, and M. Lewenstein, Phys. Rev. Lett. , 2005, 94(7): 070404
24 A. S. S?rensen, E. Demler, and M. D. Lukin, Phys. Rev. Lett. , 2005, 94(8): 086803
25 G. B. Jo, Y. R. Lee, J. H. Choi, C. A. Christensen, T. H. Kim, J. H. Thywissen, D. E. Pritchard, and W. Ketterle, Science , 2009, 325(5947): 1521
26 J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Cléent, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature , 2008, 453(7197): 891
27 G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature , 2008, 453(7197): 895
28 B. Deissler, M. Zaccanti, G. Roati, C. D’Errico, M. Fattori, M. Modugno, G. Modugno, and M. Inguscio, Nat. Phys. , 2010, 6(5): 354
29 L. Sanchez-Palencia and M. Lewenstein, Nat. Phys. , 2010, 6(2): 87
30 L. J. Garay, J. R. Anglin, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. , 2000, 85(22): 4643
31 U. R. Fischer and R. Schützhold, Phys. Rev. A , 2004, 70(6): 063615
32 M. Snoek, M. Haque, S. Vandoren, and H. T. C. Stoof, Phys. Rev. Lett. , 2005, 95(25): 250401
33 Y. Yu and K. Yang, Phys. Rev. Lett. , 2008, 100(9): 090404
34 Y. Yu and K. Yang, Phys. Rev. Lett. , 2010, 105(15): 150605
35 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science , 2004, 306(5696): 666
36 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 , 2005, 438(7065): 197
37 M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. , 2010, 82(4): 3045
38 W. Greiner, Relativistic Quantum Mechanics, 3rd Ed., Berlin: Spinger-Verleg, 2003
39 E. Schr?dinger, Sitzungsber. Preuss. Akad. Wiss. Phys.-Math. Kl. , 1930, 24: 418
40 O. Klein, Z. Phys. , 1929, 50: 157
41 S. L. Zhu, B. Wang, and L. M. Duan, Phys. Rev. Lett. , 2007, 98(26): 260402
42 E. Zhao and A. Paramekanti, Phys. Rev. Lett. , 2006, 97(23): 230404
43 C. Wu and S. Das Sarma, Phys. Rev. B , 2008, 77(23): 235107
44 B. Wunsch, F. Guinea, and F. Sols, New J. Phys. , 2008, 10(10): 103027
45 K. L. Lee, B. Grémaud, R. Han, B. G. Englert, and C. Miniatura, Phys. Rev. A , 2009, 80(4): 043411
46 A. Dutta, R. R. P. Singh, and U. Divakaran, Europhys. Lett. , 2010, 89(6): 67001
47 D. Poletti, C. Miniatura, and B. Grémaud, Europhys. Lett. , 2011, 93(3): 37008
48 D. Bercioux, D. F. Urban, H. Grabert, and W. H?usler, Phys. Rev. A , 2009, 80(6): 063603
49 D. Bercioux, N. Goldman, and D. F. Urban, Phys. Rev. A , 2011, 83(2): 023609
50 R. Shen, L. B. Shao, B. Wang, and D. Y. Xing, Phys. Rev. B , 2010, 81(4): 041410 (R)
51 I. I. Satija, D. C. Dakin, J. Y. Vaishnav, and C. W. Clark, Phys. Rev. A , 2008, 77(4): 043410
52 J. M. Hou, W. X. Yang, and X. J. Liu, Phys. Rev. A , 2009, 79(4): 043621
53 L. K. Lim, C. M. Smith, and A. Hemmerich, Phys. Rev. Lett. , 2008, 100(13): 130402
54 L. K. Lim, A. Hemmerich, and C. M. Smith, Phys. Rev. A , 2010, 81(2): 023404
55 L. K. Lim, A. Lazarides, A. Hemmerich, and C. M. Smith, Europhys. Lett. , 2009, 88(3): 36001
56 N. Goldman, A. Kubasiak, A. Bermudez, P. Gaspard, M. Lewenstein, and M. A. Martin-Delgado, Phys. Rev. Lett. , 2009, 103(3): 035301
57 X. J. Liu, X. Liu, C. Wu, and J. Sinova, Phys. Rev. A , 2010, 81(3): 033622
58 M. P. Kennett, N. Komeilizadeh, K. Kaveh, and P. M. Smith, Phys. Rev. A , 2011, 83(5): 053636
59 M. Yang and S. L. Zhu, Phys. Rev. A , 2010, 82(6): 064102
60 A. Bermudez, L. Mazza, M. Rizzi, N. Goldman, M. Lewenstein, and M. A. Martin-Delgado, Phys. Rev. Lett. , 2010, 105(19): 190404
61 L. Lepori, G. Mussardo, and A. Trombettoni, Europhys. Lett. , 2010, 92(5): 50003
62 L.M. Duan, E. Demler, and M. D. Lukin, Phys. Rev. Lett. , 2003, 91(9): 090402
63 Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature , 2005, 438(7065): 201
64 G. W. Semenoff, Phys. Rev. Lett. , 1984, 53(26): 2449
65 X. G. Wen, Quantum Field Theory of Many-Body Systems, Oxford: Oxford University, 2004
66 A. Bermudez, N. Goldman, A. Kubasiak, M. Lewenstein, and M. A. Martin-Delgado, New J. Phys. , 2010, 12(3): 033041
67 J. K. Block and N. Nygaard, Phys. Rev. A , 2010, 81(5): 053421
68 C. Wu, D. Bergman, L. Balents, and S. Das Sarma, Phys. Rev. Lett. , 2007, 99(7): 070401
69 P. Soltan-Panahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, and K. Sengstock, Nat. Phys. , 2011, 7(5): 434
70 V. Apaja, M. Hyrk?s, and M. Manninen, Phys. Rev. A , 2010, 82(4): 041402 (R)
71 D. Jaksch and P. Zoller, New J. Phys. , 2003, 5(1): 56
72 K. Osterloh, M. Baig, L. Santos, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. , 2005, 95(1): 010403
73 F. Gerbier and J. Dalibard, New J. Phys. , 2010, 12(3): 033007
74 N. Goldman, A. Kubasiak, P. Gaspard, and M. Lewenstein, Phys. Rev. A , 2009, 79(2): 023624
75 L. H. Karsten and J. Smith, Nucl. Phys. B , 1981, 183(1-2): 103
76 H. B. Nielsen and M. Ninomiya, Nucl. Phys. B , 1981, 185(1): 20
77 K. Wilson, New Phenomena in Subnuclear Physics, New York: Plenum, 1977
78 X. L. Qi, R. Li, J. Zang, and S. C. Zhang, Science , 2009, 323(5918): 1184
79 M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, Science , 2006, 311(5760): 492
80 J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. , 1999, 82(23): 4569
81 F. D. M. Haldane, Phys. Rev. Lett. , 1988, 61(18): 2015
82 M. Onoda and N. Nagaosa, Phys. Rev. Lett. , 2003, 90(20): 206601
83 C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Phys. Rev. Lett. , 2008, 101(14): 146802
84 R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, and Z. Fang, Science , 2010, 329(5987): 61
85 Z. Qiao, S. A. Yang, W. Feng, W. K. Tse, J. Ding, Y. Yao, J. Wang, and Q. Niu, Phys. Rev. B , 2010, 82(16): 161414
86 Y. Zhang and C. Zhang, Phys. Rev. B , 2011, 84(8): 085123
87 H. Li, L. Sheng, and D. Y. Xing, Phys. Rev. B , 2011, 84(3): 035310
88 L. B. Shao, S. L. Zhu, L. Sheng, D. Y. Xing, and Z. D. Wang, Phys. Rev. Lett. , 2008, 101(24): 246810
89 C. Wu, Phys. Rev. Lett. , 2008, 101(18): 186807
90 N. Gemelke, , Stanford University , 2007
91 M. Zhang, H. Hung, C. Zhang, and C. Wu, Phys. Rev. A , 2011, 83(2): 023615
93 G. Juzeliunas and P. ?hberg, Phys. Rev. Lett. , 2004, 93(3): 033602
94 G. Juzeliunas, P. ?hberg, J. Ruseckas, and A. Klein, Phys. Rev. A , 2005, 71(5): 053614
95 P. ?hberg, G. Juzeliunas, J. Ruseckas, and M. Fleischhauer, Phys. Rev. A , 2005, 72(5): 053632
96 G. Juzeliunas, J. Ruseckas, P. ?hberg, and M. Fleischhauer, Phys. Rev. A , 2006, 73(2): 025602
97 S. L. Zhu, H. Fu, C. J. Wu, S. C. Zhang, and L. M. Duan, Phys. Rev. Lett. , 2006, 97(24): 240401
98 K. J. Güunter, M. Cheneau, T. Yefsah, S. P. Rath, and J. Dalibard, Phys. Rev. A , 2009, 79(1): 011604(R)
99 J. Dalibard, F. Gerbier, G. Juzeliunas, and P. ?hberg, arXiv:cond-mat/1008.5378 , 2010
100 J. Ruseckas and G. Juzeliunas, Phys. Rev. Lett. , 2005, 95(1): 010404
101 F. Wilczek and A. Zee, Phys. Rev. Lett. , 1984, 52(24): 2111
102 G. Juzeliunas, J. Ruseckas, M. Lindberg, L. Santos, and P. ?hberg, Phys. Rev. A , 2008, 77(1): 011802(R)
103 S. L. Zhu, D. W. Zhang, and Z. D. Wang, Phys. Rev. Lett. , 2009, 102(21): 210403
104 M. Merkl, F. E. Zimmer, G. Juzeliunas, and P. ?hberg, Europhys. Lett. , 2008, 83(5): 54002
105 D. W. Zhang, Z. Y. Xue, H. Yan, Z. D. Wang, and S. L. Zhu, arXiv:1104.0444 , 2011
106 N. R. Cooper, Adv. Phys. , 2008, 57(6): 539
107 M. Burrello and A. Trombettoni, Phys. Rev. Lett. , 2010, 105(12): 125304
108 X. J. Liu, X. Liu, L. C. Kwek, and C. H. Oh, Front. Phys. China , 2008, 3(2): 113
109 I. B. Spielman, Phys. Rev. A , 2009, 79(6): 063613
110 Y. J. Lin, R. L. Compton, A. R. Perry, W. D. Phillips, J. V. Porto, and I. B. Spielman, Phys. Rev. Lett. , 2009, 102(13): 130401
111 Y. J. Lin, R. L. Compton, K. Jim′enez-Gar??a, J. V. Porto, and I. B. Spielman, Nature , 2009, 462(7273): 628
112 Y. J. Lin, R. L. Compton, K. Jim′enez-Gar??a, W. D. Phillips, J. V. Porto, and I. B. Spielman, Nat. Phys. , 2011, 7: 531
113 T. D. Stanescu, B. Anderson, and V. Galitski, Phys. Rev. A , 2008, 78(2): 023616
114 C. J. Wang, C. Gao, C. M. Jian, and H. Zhai, Phys. Rev. Lett. , 2010, 105(16): 160403
115 T. L. Ho and S. Zhang, arXiv:cond-mat/1007.0650 , 2010
116 Y. J. Lin, K. Jim′enez-Gar??a, and I. B. Spielman, Nature , 2011, 471(7336): 83
117 X. J. Liu, M. F. Borunda, X. Liu, and J. Sinova, Phys. Rev. Lett. , 2009, 102(4): 046402
118 G. Juzeliunas, J. Ruseckas, and J. Dalibard, Phys. Rev. A , 2010, 81(5): 053403
119 Z. Lan, N. Goldman, A. Bermudez, W. Lu, and P. ?hberg, Phys. Rev. B , 2011, 84(16): 165115
120 M. Merkl, A. Jacob, F. E. Zimmer, P. ?hberg, and L. Santos, Phys. Rev. Lett. , 2010, 104(7): 073603
121 L. H. Haddad and L. D. Carr, Physica D , 2009, 238(15): 1413
122 L. H. Haddad and L. D. Carr, Europhys. Lett. , 2011, 94(5): 56002
123 Z. Chen and B. Wu, Phys. Rev. Lett. , 2011, 107(6): 065301
124 See the review, W. Zawadzki and T. M. Rusin, J. Phys.: Condens. Matter , 2011, 23(14): 143201
125 J. Schliemann, D. Loss, and R. M. Westervelt, Phys. Rev. Lett. , 2005, 94(20): 206801
126 M. I. Katsnelson, Eur. Phys. J. B , 2006, 51(2): 157
127 B. Trauzettel, Y. M. Blanter, and A. F. Morpurgo, Phys. Rev. B , 2007, 75(3): 035305
128 D. Lurié and S. Cremer, Physica , 1970, 50(2): 224
129 X. Zhang, Phys. Rev. Lett. , 2008, 100(11): 113903
130 F. Dreisow, M. Heinrich, R. Keil, A. T¨unnermann, S. Nolte, S. Longhi, and A. Szameit, Phys. Rev. Lett. , 2010, 105(14): 143902
131 L. Lamata, J. León, T. Sch¨atz, and E. Solano, Phys. Rev. Lett. , 2007, 98(25): 253005
132 J. Y. Vaishnav and C. W. Clark, Phys. Rev. Lett. , 2008, 100(15):
133 J. J. Song and B. A. Foreman, Phys. Rev. A , 2009, 80(4): 045602
134 Q. Zhang, J. Gong, and C. H. Oh, Phys. Rev. A , 2010, 81(2): 023608
135 D. Witthaut, Phys. Rev. A , 2010, 82(3): 033602
136 J. Larson, J. P. Martikainen, A. Collin, and E. Sj?qvist, Phys. Rev. A , 2010, 82(4): 043620
137 M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat. Phys. , 2006, 2(9): 620
138 O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, M. Segev, and T. Pereg-Barnea, Phys. Rev. Lett. , 2010, 104(6): 063901
139 D. Witthaut, T. Salger, S. Kling, C. Grossert, and M. Weitz, Phys. Rev. A , 2011, 84(3): 033601
140 T. Salger, C. Grossert, S. Kling, and M. Weitz, arXiv:condmat/1108.4447 , 2011
141 J. Otterbach, R. G. Unanyan, and M. Fleischhauer, Phys. Rev. Lett. , 2009, 102(6): 063602
142 M. G. Tarallo, J. Miller, J. Agresti, E. D’Ambrosio, R. De-Salvo, D. Forest, B. Lagrange, J. M. Mackowsky, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remilleux, B. Simoni, and P. Willems, Appl. Opt. , 2007, 46(26): 6648
143 L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, and C. Salomon, Science , 2002, 296(5571): 1290
144 N. Dombey, P. Kennedy, and A. Calogeracos, Phys. Rev. Lett. , 2000, 85(9): 1787
145 F. Wilczek, Nat. Phys. , 2009, 5(9): 614
146 R. F. Service, Science , 2011, 332(6026): 193
147 S. L. Zhu, L. B. Shao, Z. D. Wang, and L. M. Duan, Phys. Rev. Lett. , 2011, 106(10): 100404
148 L. Jiang, T. Kitagawa, J. Alicea, A. R. Akhmerov, D. Pekker, G. Refael, J. I. Cirac, E. Demler, M. D. Lukin, and P. Zoller, Phys. Rev. Lett. , 2011, 106(22): 220402
149 S. Tewari and S. Das Sarma, Phys. Rev. Lett. , 2007, 98(1): 010506
150 C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys. , 2008, 80(3): 1083
151 J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, Nat. Phys. , 2011, 7(5): 412
152 J. Casanova, C. Sabin, J. Leon, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcia-Ripoll, and E. Solano, arXiv:1102.1651 , 2011
153 J. I. Cirac, P. Maraner, and J. K. Pachos, Phys. Rev. Lett. , 2010, 105(19): 190403
[1] Zi-jing DING (丁子敬), Yang JIAO (焦扬), Sheng MENG (孟胜). Quantum simulation of molecular interaction and dynamics at surfaces[J]. Front. Phys. , 2011, 6(3): 294-308.
[2] Xin-hua PENG (彭新华), Dieter SUTER, . Spin qubits for quantum simulations [J]. Front. Phys. , 2010, 5(1): 1-25.
[3] LIU Xiong-jun, LIU Xin, KWEK Leong-Chuan, OH ChooHiap. Manipulating atomic states via optical orbital angular-momentum[J]. Front. Phys. , 2008, 3(2): 113-125.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed