Light-induced gauge fields for ultracold atoms

Reports on Progress in Physics

Volumn 77, Issue 12, 2014, Pages

  Goldman, N ^a   Juzeliunas, G ^b   Ohberg P ^c   Spielman, I B ^d  

^a Paris Sciences et Lettres   (France)

^b VILNIUS UNIVERSITY   (Lithuania)

^c HERIOT WATT UNIVERSITY   (United Kingdom)

^d UNIVERSITY OF MARYLAND   (United States)

Author keywords

gauge potentials; light matter interaction; ultracold atoms

Indexed keywords

EID: 84918574927     PISSN: 00344885     EISSN: None     Source Type: Journal    
DOI: 10.1088/0034-4885/77/12/126401     Document Type: Review

References (501)

1. Anderson M H, Ensher J R, Matthews M R, Wieman C E and Cornell E A 1995 Science 269 198
2. Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M and Ketterle W 1995 Phys. Rev. Lett. 75 3969-73
3. DeMarco B and Jin D S 1999 Science 285 1703-6
4. Ketterle W and Miesner H J 1996 Phys. Rev. A 56 3291
5. Jeltes T et al 2007 Nature 445 402-5
6. Fisher M P A, Weichman P B, Grinstein G and Fisher D S 1989 Phys. Rev. B 40 546-70
7. Jaksch, Bruder C, Cirac J, Gardiner C and Zoller P 1998 Phys. Rev. Lett. 81 3108
8. Greiner M, Mandel O, Esslinger T, Hänsch T and Bloch I 2002 Nature 415 39-44
9. Greiner M, Regal C A and Jin D S 2003 Nature 426 537-40
10. Bourdel T, Khaykovich L, Cubizolles J, Zhang J, Chevy F, Teichmann M, Tarruell L, Kokkelmans S and Salomon C 2004 Phys. Rev. Lett. 93 050401
11. Bartenstein M, Altmeyer A, Riedl S, Jochim S, Chin C, Denschlag J and Grimm R 2004 Phys. Rev. Lett. 92 120401
12. Zwierlein M, Stan C, Schunck C, Raupach S, Kerman A and Ketterle W 2004 Phys. Rev. Lett. 92 120403
13. Kinast J, Hemmer S, Gehm M, Turlapov A and Thomas J 2004 Phys. Rev. Lett. 92 150402
14. Bissbort U, Götze S, Li Y, Heinze J, Krauser J S, Weinberg M, Becker C, Sengstock K and Hofstetter W 2011 Phys. Rev. Lett. 106 205303
15. Endres M, Fukuhara T, Pekker D, Cheneau M, Schau P, Gross C, Demler E, Kuhr S and Bloch I 2012 Nature 487 454-8
16. Williams J, Hazlett E, Huckans J, Stites R, Zhang Y and O'Hara K 2009 Phys. Rev. Lett. 103 130404
17. Kapit E and Mueller E 2011 Phys. Rev. A 83 033625
18. Banerjee D, Bögli M, Dalmonte M, Rico E, Stebler P, Wiese U J and Zoller P 2013 Phys. Rev. Lett. 110 125303
19. Edmonds M J, Valiente M, Juzeliunas G, Santos L and Öhberg P 2013 Phys. Rev. Lett. 110 085301
20. Bermudez A, Mazza L, Rizzi M, Goldman N, Lewenstein M and Martin-Delgado M 2010 Phys. Rev. Lett. 105 190404
21. Lin Y J, Compton R L, Perry A R, Phillips W D, Porto J V and Spielman I B 2009 Phys. Rev. Lett. 102 130401
22. Lin Y J, Compton R L, Jimenez-Garcia K, Porto J V and Spielman I B 2009 Nature 462 628-32
23. Lin Y J, Compton R L, Jimenez-Garcia K, Phillips W D, Porto J V and Spielman I B 2011 Nature Phys. 7 531-4
24. Wilczek F and Zee A 1984 Phys. Rev. Lett. 52 2111-4
25. Lin Y J, Jiménez-García K and Spielman I B 2011 Nature 471 83-6
26. Wang P, Yu Z Q, Fu Z, Miao J, Huang L, Chai S, Zhai H and Zhang J 2012 Phys. Rev.. Lett. 109 095301
27. Cheuk L W, Sommer A T, Hadzibabic Z, Yefsah T, Bakr W S and Zwierlein M W 2012 Phys. Rev. Lett 109 095302
28. Zhang J Y et al 2012 Phys. Rev. Lett. 109 115301
29. Fu Z, Huang L, Meng Z, Wang P, Zhang L, Zhang S, Zhai H, Zhang P and Zhang J 2014 Nature Phys. 10 110
30. Zhang L, Zhang J Y, Ji S C, Du Z D, Zhai H, Deng Y, Chen S, Zhang P and Pan J W 2013 Phys. Rev. A 87 011601(R)
31. Qu C, Hamner C, Gong M, Zhang C and Engels P 2013 Phys. Rev. A 88 021604
32. LeBlanc L J, Beeler M C, Jimenez-Garcia K, Perry A R, Sugawa S, Williams R A and Spielman I B 2013 New J. Phys. 15 073011
33. Lewenstein M, Sanpera A, Ahufinger V, Damski B, De A S and Sen U 2007 Adv. Phys. 56 243-379
34. Bloch I, Dalibard J and Zwerger W 2008 Rev. Mod. Phys. 80 885
35. Lewenstein M, Sanpera A and Ahufinger V 2012 Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems (Oxford: Oxford University Press)
36. Görlitz A et al 2001 Phys. Rev. Lett. 87 130402
37. Chin C, Grimm R, Julienne P and Tiesinga E 2010 Rev. Mod. Phys. 82 1225
38. Feynman R P 1982 Int. J. Theor. Phys. 21 467
39. Mead C A and Truhlar D G 1979 J. Chem. Phys. 70 2284-96
40. Berry M V 1980 Eur. J. Phys. 1 240
41. Berry M 1984 Proc. R. Soc. Lond. A 392 45
42. Mead C 1992 Rev. Mod. Phys. 64 51
43. Shapere A and Wilczek F (ed) 1989 Geometric Phases in Physics (Singapore: World Scientific)
44. Bohm A, Mostafazadeh A, Koizumi H, Niu Q and Zwanziger J 2003 Geometric Phases in Quantum Systems (Berlin: Springer)
45. Taichenachev A V, Tumaikin A M and Yudin V I 1992 Laser Phys. 2 575
46. Dum R and Olshanii M 1996 Phys. Rev. Lett. 76 1788-91
47. Visser P M and Nienhuis G 1998 Phys. Rev. A 57 4581-91
48. Juzeliunas G and Öhberg P 2004 Phys. Rev. Lett. 93 033602
49. Juzeliunas G, Ruseckas J, Öhberg P and Fleischhauer M 2006 Phys. Rev. A 73 025602
50. Zhu S L, Fu H, Wu C J, Zhang S C and Duan L M 2006 Phys. Rev. Lett. 97 240401
51. Spielman I B 2009 Phys. Rev. A 79 063613
52. Günter K J, Cheneau M, Yefsah T, Rath S P and Dalibard J 2009 Phys. Rev. A 79 011604
53. Dutta S K, Teo B K and Raithel G 1999 Phys. Rev. Lett. 83 1934-7
54. Unanyan R G, Shore B W and Bergmann K 1999 Phys. Rev. A 59 2910
55. Ruseckas J, Juzeliunas G, Öhberg P and Fleischhauer M 2005 Phys. Rev. Lett. 95 010404
56. Liu X J, Borunda M F, Liu X and Sinova J 2009 Phys. Rev. Lett. 102 046402
57. Liu X J, Liu X, Kwek L C and Oh C H 2007 Phys. Rev. Lett. 98 026602
58. Beeler M C, Williams R A, Jimenez-Garcia K, LeBlanc L J, Perry A R and Spielman I B 2013 Nature 498 201-4
59. Eckardt A, Weiss C and Holthaus M 2005 Phys. Rev. Lett. 95 260404
60. Cooper N R 2008 Adv. Phys. 57 539-616
61. Aidelsburger M, Atala M, Nascimbène S, Trotzky S, Chen Y A and Bloch I 2011 Phys. Rev. Lett. 107 255301
62. Jiménez-García K, LeBlanc L, Williams R, Beeler M, Perry A and Spielman I B 2012 Phys. Rev. Lett. 108 225303
63. Struck J, Ölschläger C, Weinberg M, Hauke P, Simonet J, Eckardt A, Lewenstein M, Sengstock K and Windpassinger P 2012 Phys. Rev. Lett. 108 225304
64. Aidelsburger M, Atala M, Lohse M, Barreiro J T, Paredes B and Bloch I 2013 Phys. Rev. Lett. 111 185301
65. Miyake H, Siviloglou G A, Kennedy C J, Burton W C and Ketterle W 2013 Phys. Rev. Lett. 111 185302
66. Cheng T P and Li L F 1991 Gauge Theory of Elementary Particle Physics (Oxford: Oxford University Press)
67. Levin M and Wen X G 2005 Rev. Mod. Phys. 77 871-9
68. Wiese U J 2013 Ann. Phys. 525 777
69. Banerjee D, Dalmonte M, Müller M, Rico E, Stebler P, Wiese U J and Zoller P 2012 Phys. Rev. Lett. 109 175302
70. Tagliacozzo L, Celi A, Orland P, Mitchell M W and Lewenstein M 2013 Nature Commun. 4 2615
71. Zohar E, Cirac J I and Reznik B 2013 Phys. Rev. Lett. 110 125304
72. Tagliacozzo L, Celi A, Zamora A and Lewenstein M 2013 Ann. Phys. 330 160-91
73. Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057-110
74. Hasan M and Kane C 2010 Rev. Mod. Phys. 82 3045-67
75. Nayak C, Simon S H, Stern A, Freedman M and Das Sarma S 2008 Rev. Mod. Phys. 80 1083
76. Nakahara M 2003 Geometry, Topology, and Physics (Graduate Student Series in Physics) (Bristol: Institute of Physics Publishing) ISBN: ISBN 9780750306065
77. von Klitzing K 1986 Rev. Mod. Phys. 58 519-31
78. Hatsugai Y 1993 Phys. Rev. Lett. 71 3697-700
79. Wen X G 1995 Adv. Phys. 44 405
80. Dalibard J, Gerbier F, Juzeliunas G and Öhberg P 2011 Rev. Mod. Phys. 83 1523-43
81. Fetter A L 2009 Rev. Mod. Phys. 81 647
82. Landau L D and Lifshitz E M 1987 Quantum Mechanics (New York: Pergamon)
83. Matthews M R, Anderson B P, Haljan P C, Hall D S, Wieman C E and Cornell E A 1999 Phys. Rev. Lett. 83 2498-501
84. Madison K W, Chevy F, Wohlleben W and Dalibard J 2000 Phys. Rev. Lett. 84 806-9
85. Abo-Shaeer J R, Raman C, Vogels J M and Ketterle W 2001 Science 292 476-9
86. Tung S, Schweikhard V and Cornell E A 2006 Phys. Rev. Lett. 97 240402
87. Williams R A, Al-Assam S and Foot C J 2010 Phys. Rev. Lett. 104 050404
88. Wright K C, Blakestad R B, Lobb C J, Phillips W D and Campbell G K 2012 Phys. Rev. Lett. 110 025302
89. Engels P, Coddington I, Haljan P, Schweikhard V and Cornell E 2003 Phys. Rev. Lett. 90 170405
90. Schweikhard V, Coddington I, Engels P, Mogendorff V P and Cornell E A 2004 Phys. Rev. Lett. 92 040404
91. Chevy F, Madison K W and Dalibard J 2000 Phys. Rev. Lett. 85 2223-7
92. Haljan P C, Anderson B P, Coddington I and Cornell E A 2001 Phys. Rev. Lett. 86 2922-5
93. Gemelke N, Sarajlic E and Chu S 2010 arXiv:1007.2677
94. Madison K W, Fischer M C, Diener R B, Niu Q and Raizen M G 1998 Phys. Lett. Lett. 81 5093
95. Struck J, Ölschläger C, Targat R L, Soltan-Panahi P, Eckardt A, Lewenstein M, Windpassinger P and Sengstock K 2011 Science 333 996
96. Arimondo E, Ciampinia D, Eckardt A, Holthaus M and Morsch O 2012 Adv. At. Mol. Opt. Phys. 61 515
97. Struck J et al 2013 Nature Phys. 9 738-43
98. Windpassinger P and Sengstock K 2013 Rep. Prog. Phys. 76 086401
99. Dalibard J 2013 Cours du Collège de France (www.phys.ens.fr/∼ dalibard/CdF/2013/Cours-2013.pdf)
100. Hauke P et al 2012 Phys. Rev. Lett. 109 145301
101. Goldman N and Dalibard J 2014 Phys. Rev. X 4 031027
102. Zheng W and Zhai H 2014 Phys. Rev. A 89 061603
103. Baur S K, Schleier-Smith M H and Cooper N R 2014 Phys. Rev. A 89 051605
104. Anisimovas E, Anderson B, Juzeliunas G and Eckardt A 2014 in preparation
105. Kitagawa T, Berg E, Rudner M and Demler E 2010 Phys. Rev. B 82 235114
106. Lindner N H, Refael G and Galitski V 2011 Nature Phys. 7 490
107. Cayssol J, Dóra B, Simon F and Moessner R 2013 Phys. Status Solidi (RRL) 7 101-8
108. Levy N, Burke S A, Meaker K L, Panlasigui M, Zettl A, Guinea F, Castro Neto A H and Crommie M F 2010 Science 329 544
109. Oka T and Aoki H 2009 Phys. Rev. B 79 081406(R)
110. Cohen-Tannoudji C, Dupont-Roc J and Grynberg G 1989 Photons and Atoms: Introduction to Quantum Electrodynamics (New York: Wiley)
111. Jackson J D 1998 Classical Electrodynamics (New York: Wiley)
112. Moody J, Shapere A and Wilczek F 1986 Phys. Rev. Lett. 56 893
113. Zygelman B 1987 Phys. Lett. A 125 476
114. Zee A 1988 Phys. Rev. A 38 1
115. Jackiw R 1988 Comments At. Mol. Phys. 21 71
116. Xiao D, Chang M C and Niu Q 2010 Rev. Mod. Phys. 82 1959
117. Zygelman B 2012 Phys. Rev. A 86 042704
118. Grynberg G and Robilliard C 2001 Phys. Rep. 355 335
119. Dudarev A M, Diener R B, Carusotto I and Niu Q 2004 Phys. Rev. Lett. 92 153005
120. Zhang P, Li Y and Sun C P 2005 Eur. Phys. J. D 36 229
121. Liu X J, Liu X, Kwek L C and Oh C H 2008 Front. Phys. China 3 113-25
122. Aharonov Y and Stern A 1992 Phys. Rev. Lett. 69 3593-7
123. Cheneau M, Rath S P, Yefsah T, Gunter K J, Juzeliunas G and Dalibard J 2008 Europhys. Lett. 83 60001
124. Unanyan R G, Fleischhauer M, Shore B W and Bergmann K 1998 Opt. Commun. 155 144
125. Juzeliunas G, Ruseckas J, Öhberg P and Fleischhauer M 2007 Lithuanian J. Phys. 47 351-60
126. Zhang X D, Wang Z D, Hu L B, Zhang Z M and Zhu S L 2008 New J. Phys. 10 043031
127. Fu Z, Huang L, Meng Z, Wang P, Liu X J, Pu H, Hu H and Zhang J 2013 Phys. Rev. A 87 053619
128. Lu L H and Li Y Q 2007 Phys. Rev. A 76 023410
129. Burrello M and Trombettoni A 2010 Phys. Rev. Lett. 105 125304
130. Radic J, Sedrakyan T A, Spielman I B and Galitski V 2011 Phys. Rev. A 84 063604
131. Zhou X F, Zhou J and Wu C 2011 Phys. Rev. A 84 063624
132. Xu X Q and Han J H 2011 Phys. Rev. Lett. 107 200401
133. Liu C F and Liu W M 2012 Phys. Rev. A 86 033602
134. Zhang X F, Gao R S, Wang X, Dong R F, Liu T and Zhang S G 2013 Phys. Lett. A 377 1109
135. Huckans J H, Spielman I B, Tolra B L, Phillips W D and Porto J V 2009 Phys. Rev. A 80 043609
136. Happer W and Mathur B 1967 Phys. Rev. 163 12
137. Cohen-Tannoudji C and Dupont-Roc J 1972 Phys. Rev. A 5 968-84
138. Deutsch I H and Jessen P S 1998 Phys. Rev. A 57 1972-86
139. Grimm R, Weidemüller M and Ovchinnikov Y B 2000 Adv. At. Mol. Opt. Phys. 42 95-170
140. Cui X, Biao L, Ho T L, Lev B L and Zhai H 2013 Phys. Rev. A 88 011601(R)
141. Cohen-Tannoudji C, Dupont-Roc J and Grynberg G 1998 Atom-Photon Interactions (Weinheim: Wiley-VCH)
142. Loudon R 2000 The Quantum Theory of Light 3rd edn (Oxford: Oxford University Press)
143. Sebby-Strabley J, Anderlini M, Jessen P S and Porto J V 2006 Phys. Rev. A 73 033605
144. Juzeliunas G and Spielman I B 2012 New J. Phys. 14 123022
145. Breit G and Rabi I I 1931 Phys. Rev. 38 2082-3
146. Budker D, Kimball D and DeMille D 2004 Atomic Physics: An Exploration through Problems and Solutions (Oxford: Oxford University Press)
147. LeBlanc L J, Jiménez-García K, Williams R A, Beeler M C, Perry A R, Phillips W D and Spielman I B 2012 Proc. Natl Acad. Sci. USA 109 10811
148. McKay D and DeMarco B 2010 New J. Phys. 12 055013
149. Williams R A, LeBlanc L J, Jiménez-García K, Beeler M C, Perry A R, Phillips W D and Spielman I B 2012 Science 335 314-7
150. Cooper N R and Dalibard J 2011 Europhys. Lett 95 66004
151. Juzeliunas G, Öhberg P, Ruseckas J and Klein A 2005 Phys. Rev. A 71 053614
152. Juzeliunas G, Ruseckas J and Öhberg P 2005 J. Phys. B: At. Mol. Opt. Phys. 38 4171
153. Song J J, Foreman B A, Liu X J and Oh C H 2008 Europhys. Lett. 84 20012
154. Cooper N R and Hadzibabic Z 2010 Phys. Rev. Lett. 104 030401
155. Arimondo E 1996 Progress in Optics vol 35 ed E Wolf (Amsterdam: Elsevier) p 259
156. Harris S E 1997 Phys. Today 50 36
157. Lukin M D 2003 Rev. Mod. Phys. 75 457-72
158. Fleischhauer M, Imamoglu A and Marangos J P 2005 Rev. Mod. Phys. 77 633
159. Bergmann K, Theuer H and Shore B W 1998 Rev. Mod. Phys. 70 1003-25
160. Vitanov N V, Fleischhauer M, Shore B W and Bergmann K 2001 Adv. At. Mol. Opt. Phys. 46 55
161. Král P, Thanopulos I and Shapiro M 2007 Rev. Mod. Phys. 79 53
162. Stanescu T D and Galitski V 2007 Phys. Rev. B 75 125307
163. Jacob A, Öhberg P, Juzeliunas G and Santos L 2007 Appl. Phys. B 89 439
164. Juzeliunas G, Ruseckas J, Lindberg M, Santos L and Öhberg P 2008 Phys. Rev. A 77 011802(R)
165. Stanescu T D, Anderson B and Galitski V 2008 Phys. Rev. A 78 023616
166. Vaishnav J Y and Clark C W 2008 Phys. Rev. Lett. 100 153002
167. Juzeliunas G, Ruseckas J and Dalibard J 2010 Phys. Rev. A 81 053403
168. Campbell D L, Juzeliunas G and Spielman I B 2011 Phys. Rev. A 84 025602
169. Galitski V and Spielman I B 2013 Nature 494 49-54
170. Juzeliunas G and Öhberg P 2008 Structured Light and its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces ed D L Andrews (Amsterdam: Elsevier) pp 295-333
171. Li Y, Bruder C and Sun C P 2007 Phys. Rev. Lett. 99 130403
172. Bohm A, Kendrick B, Loewe M and Boya L 1992 J. Math. Phys. 33 977
173. Zygelman B 1990 Phys. Rev. Lett. 64 256
174. Cooper N 2011 Phys. Rev. Lett. 106 175301
175. Juzeliunas G and Spielman I B 2012 Proc. SPIE 8274 882740H
176. Hemmerich A, Donald Schropp J and Hänsch T W 1991 Phys. Rev. A 44 1910
177. Hemmerich A, Schropp D, Esslinger T and Hansch T W 1992 Europhys. Lett. 18 391
178. Cooper N R and Dalibard J 2013 Phys. Rev. Lett. 110 185301
179. Jaksch D and Zoller P 2003 New J. Phys. 5 56
180. Gerbier F and Dalibard J 2010 New J. Phys. 12 033007
181. Cooper N R and Moessner R 2012 Phys. Rev. Lett. 109 215302
182. Haldane F D M 1988 Phys. Rev. Lett. 61 2015
183. Higbie J and Stamper-Kurn D M 2002 Phys. Rev. Lett. 88 090401
184. Papoff F, Mauri F and Arimondo E 1992 J. Opt. Soc. Am. B 9 321-31
185. Montina A and Arecchi F T 2003 Phys. Rev. A 67 023616
186. Higbie J and Stamper-Kurn D M 2004 Phys. Rev. A 69 053605
187. Spielman I B, Johnson P R, Huckans J H, Fertig C D, Rolston S L, Phillips W D and Porto J V 2006 Phys. Rev. A 73 020702(R)
188. Yarmchuk E J, Gordon M J V and Packard R E 1979 Phys. Rev. Lett. 43 214-7
189. Ol'shanii M A and Minogin V G 1991 Quantum Opt. 3 317
190. Kulin S, Castin Y, Ol'shanii M, Peik E, Saubaméa B, Leduc M and Cohen-Tannoudji C 1999 Eur. Phys. J. D 7 279
191. Unanyan R G and Fleischhauer M 2004 Phys. Rev. A 69 050302(R)
192. Theuer H, Unanyan R, Habscheid C, Klein K and Bergmann K 1999 Opt. Express 4 77
193. Vewinger F, Heinz M, Fernandez R G, Vitanov N V and Bergmann K 2003 Phys. Rev. Lett. 91 213001
194. Pietilä V and Möttönen M 2009 Phys. Rev. Lett. 102 080403
195. Song J J and Foreman B A 2009 Phys. Rev. A 80 033602
196. Juzeliunas G, Ruseckas J, Jacob A, Santos L and Öhberg P 2008 Phys. Rev. Lett. 100 200405
197. Koralek J D, Weber C P, Orenstein J, Bernevig B A, Zhang S C, Mack S and Awschalom D D 2009 Nature 458 610-3
198. Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802
199. Schnyder A P, Ryu S, Furusaki A and Ludwig A W W 2008 Phys. Rev. B 78 195125
200. Sau J D, Tewari S, Lutchyn R M, Stanescu T D and Das Sarma S 2010 Phys. Rev. B 82 214509
201. Osterloh K, Baig M, Santos L, Zoller P and Lewenstein M 2005 Phys. Rev. Lett. 95 010403
202. Goldman N, Satija I, Nikolic P, Bermudez A, Martin-Delgado M A, Lewenstein M and Spielman I B 2010 Phys. Rev. Lett. 105 255302
203. Anderson B M, Spielman I B and Juzeliunas G 2013 Phys. Rev. Lett. 111 125301
204. Xu Z F, You L and Ueda M 2013 Phys. Rev. A 87 063634
205. Stanescu T D, Zhang C and Galitski V 2007 Phys. Rev. Lett. 99 110403
206. Ho T L and Zhang S 2012 Phys. Rev. Lett. 107 150403
207. Li Y, Pitaevskii L P and Stringari S 2012 Phys. Rev. Lett. 108 225301
208. Han L and Sá de Melo C A R 2012 Phys. Rev. A 85 011606
209. Seo K, Han L and Sá de Melo C A R 2012 Phys. Rev. A 85 033601
210. Seo K, Han L and Sá de Melo C A R 2012 Phys. Rev. Lett. 109 105303
211. Li Y, Martone G I and Stringari S 2012 Europhys. Lett. 99 56008
212. Martone G I, Li Y, Pitaevskii L P and Stringari S 2012 Phys. Rev. A 86 063621
213. Ozawa T, Pitaevskii L P and Stringari S 2013 Phys. Rev. A 87 063610
214. Li Y, Martone G I, Pitaevskii L P and Stringari S 2013 Phys. Rev. Lett. 110 235302
215. Lin Y J, Perry A R, Compton R L, Spielman I B and Porto J V 2009 Phys. Rev. A 79 063631
216. Zhai H 2012 Int. J. Mod. Phys. B 26 1230001
217. Xu Z F and You L 2012 Phys. Rev. A 85 043605
218. Liu X J, Law K T and Ng T K 2014 Phys. Rev. Lett. 112 086401
219. Sun Q, Wen L, Liu W M, Juzeliunas G and Ji A C 2014 arXiv:1403.4338
220. Anderson B M, Juzeliunas G, Galitski V M and Spielman I B 2012 Phys. Rev. Lett. 108 235301
221. Vyasanakere J P and Shenoy V B 2011 Phys. Rev. B 83 94515
222. Vyasanakere J P, Zhang S and Shenoy V B 2011 Phys. Rev. B 84 14512
223. Jiang L, Liu X J, Hu H and Pu H 2011 Phys. Rev. A 84 063618
224. Hu H, Jiang L, Liu X J and Pu H 2011 Phys. Rev. Lett. 107 195304
225. Liu X J, Jiang L, Pu H and Hu H 2012 Phys. Rev. A 85 21603
226. Chen G, Gong M and Zhang C 2012 Phys. Rev. A 85 013601
227. He L and Huang X G 2012 Phys. Rev. Lett. 108 145302
228. He L and Huang X G 2012 Phys. Rev. B 86 014511
229. Cui J X, Liu X J, Long G L and Hu H 2012 Phys. Rev. A 86 053628
230. Zheng Z, Gong M, Zou X, Zhang C and Guo G 2013 Phys. Rev. A 87 031602
231. Maldonado-Mundo D, He L, Öhberg P and Valiente M 2013 Phys. Rev. A 88 053609
232. Sinha S, Nath R and Santos L 2011 Phys. Rev. Lett. 107 270401
233. C Wu I, Mondragon -Shem and Zhou X F 2011 Chin. Phys. Lett. 28 097102
234. Hu H, Ramachandhran B, Pu H and Liu X J 2012 Phys. Rev. Lett. 108 010402
235. Su S W, Liu I K, Tsai Y C, Liu W M and Gou S C 2012 Phys. Rev. A 86 023601
236. Kawakami T, Mizushima T, Nitta M and Machida K 2012 Phys. Rev. Lett. 109 015301
237. Ruokokoski E, Huhtamäki J A M and Möttönen M 2012 Phys. Rev. A 86 051607
238. Xu Z F, Kawaguchi Y, You L and Ueda M 2012 Phys. Rev. A 86 033628
239. Sedrakyan T A, Kamenev A and Glazman L I 2012 Phys. Rev. A 86 063639
240. Song S W, Zhang Y C, Wen L, Wang H, Sun Q, Ji A C and Liu W M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 145304
241. Su S W, Gou S C, Spielman I B, Santos L, Acus A, Ruseckas J and Juzeliunas G 2014 in preparation
242. Zhai H 2014 arXiv:1403.8021
243. Zhou X, Li Y, Cai Z and Wu C 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134001
244. Gerbier F, Goldman N, Lewenstein M and Sengstock K 2013 J. Phys. B: At. Mol. Opt. Phys. 46 130201
245. Stringari S 1996 Phys. Rev. Lett. 77 2360-3
246. Öhberg P, Surkov E L, Tittonen I, Stenholm S, Wilkens M and Shlyapnikov G V 1997 Phys. Rev. A 56 R3346-9
247. Fliesser M, Csordás A, Szépfalusy P and Graham R 1997 Phys. Rev. A 56 R2533-6
248. Wang C, Gao C, Jian C M and Zhai H 2010 Phys. Rev. Lett. 105 160403
249. Barnett R, Powell S, Grass T, Lewenstein M and Das Sarma S 2012 Phys. Rev. A 85 023615
250. Zhang Y, Mao L and Zhang C 2012 Phys. Rev. Lett. 108 035302
251. Ozawa T and Baym G 2012 Phys. Rev. A 85 013612
252. Ozawa T and Baym G 2012 Phys. Rev. A 85 063623
253. Zhou X F, Zhou J and Wu C 2011 Phys. Rev. A 84 63624
254. Cui X and Zhou Q 2013 Phys. Rev. A 87 31604
255. He P S, Liao R and Liu W M 2012 Phys. Rev. A 86 43632
256. Liao R, Huang Z G, Lin X M and Liu W M 2013 Phys. Rev. A 87 043605
257. Han W, Juzeliunas G, Zhang W and Liu W M 2014 arXiv:1407.2972
258. Zhou Q and Cui X 2013 Phys. Rev. Lett. 110 140407
259. Chen X, Rabinovich M, Anderson B M and Santos L 2014 arXiv:1406.4938
260. Lan Z and Öhberg P 2014 Phys. Rev. A 89 023630
261. Osterloh K, Baig M, Santos L, Zoller P and Lewenstein M 2005 Phys. Rev. Lett. 95 010403
262. Cong-Jun W, Mondragon-Shem I and Xiang-Fa Z 2011 Chin. Phys. Lett. 28 097102
263. Nayak C, Simon S H, Stern A, Freedman M and Das Sarma S 2008 Rev. Mod. Phys. 80 1083
264. Salomaa M M and Volovik G E 1985 Phys. Rev. Lett. 55 1184
265. Gopalakrishnan S, Martin I and Demler E A 2013 Phys. Rev. Lett. 111 185304
266. Wilson R M, Anderson B M and Clark C W 2013 Phys. Rev. Lett. 111 185303
267. Jochim S, Bartenstein M, Altmeyer A, Hendl G, Riedl S, Chin C, Denschlag J H and Grimm R 2003 Science 302 2101
268. Zwierlein M W, Abo-Shaeer J R, Schirotzek A, Schunck C H and Ketterle W 2003 Nature 435 1047
269. Gor'kov L P and Rashba E I 2001 Phys. Rev. Lett. 87 37004
270. Yu Z Q and Zhai H 2011 Phys. Rev. Lett. 107 195305
271. Shenoy V B and Vyasanakere J P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134009
272. Zhou K and Zhang Z 2012 Phys. Rev. Lett. 108 025301
273. Sun Q, Zhu G B, Liu W M and Ji A C 2013 Phys. Rev. A 88 063637
274. Gopalakrishnan S, Lamacraft A and Goldbart P M 2011 Phys. Rev. A 84 061604
275. Ozawa T and Baym G 2011 Phys. Rev. A 84 043622
276. Maldonado-Mundo D, Öhberg P and Valiente M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134002
277. Sato M, Takahashi Y and Fujimoto S 2009 Phys. Rev. Lett. 103 020401
278. Sau J, Sensarma R, Powell S, Spielman I and Das Sarma S 2011 Phys. Rev. B 83 140510
279. Zhang C, Tewari S, Lutchyn R M and Das Sarma S 2008 Phys. Rev. Lett. 101 160401
280. Gong M, Tewari S and Zhang C 2011 Phys. Rev. Lett. 107 195303
281. Iskin M and Subaş i A L 2011 Phys. Rev. Lett. 107 050402
282. Liao R, Yi-Xiang Y and Liu W M 2012 Phys. Rev. Lett. 108 80406
283. Zheng Z, Gong M, Zou X, Zhang C and Guo G 2013 Phys. Rev. A 87 031602
284. Zheng Z, Gong M, Zhang Y, Zou X, Zhang C and Guo G 2012 arXiv:1212.6826
285. Dong L, Jiang L, Hu H and Pu H 2013 Phys. Rev. A 87 043616
286. Shenoy V 2013 Phys. Rev. A 88 033609
287. Liu X J and Hu H 2012 Phys. Rev. A 85 033622
288. Zinn-Justin J 2002 Quantum Field Theory and Critical Phenomena (International Series of Monographs on Physics) 4th edn (Oxford: Clarendon)
289. Wilson K G 1974 Phys. Rev. D 10 2445
290. Gupta R 1998 arXiv:hep-lat/9807028
291. Kogut J B 1983 Rev. Mod. Phys. 55 775
292. Ashcroft N W and Mermin D N 1976 Solid State Physics 1st edn (Toronto: Thomson Learning)
293. Mott N 1968 Rev. Mod. Phys. 40 677
294. Lee P, Nagaosa N and Wen X 2006 Rev. Mod. Phys. 78 17
295. Neto A H C, Guinea F, Peres N M R, Novoselov K S and Geim A K 2009 Rev. Mod. Phys. 81 109
296. Qi X L, Hughes T L and Zhang S C 2008 Phys. Rev. B 78 195424
297. Jaksch D and Zoller P 2005 Ann. Phys. 315 52-79
298. Jördens R, Strohmaier N, Günter K, Moritz H and Esslinger T 2008 Nature 455 204-7
299. Wannier G 1937 Phys. Rev. 52 191
300. Kohn W 1959 Phys. Rev. 115 1460
301. Altman E, Hofstetter W, Demler E and Lukin M D 2003 New J. Phys. 5 113
302. Tarruell L, Greif D, Uehlinger T, Jotzu G and Esslinger T 2012 Nature 483 302
303. Schneider U, Hackermüller L, Ronzheimer J P, Will S, Braun S, Best T, Bloch I, Demler E, Mandt S, Rasch D and Rosch A 2012 Nature Phys. 8 213
304. Eckardt A, Hauke P, Soltan-Panahi P, Becker C, Sengstock K and Lewenstein M 2010 Europhys. Lett. 89 10010
305. Hofstadter D 1976 Phys. Rev. B 14 2239
306. Dirac P 1931 Proc. R. Soc. Lond. A 133 60
307. Aharonov Y and Bohm D 1959 Phys. Rev. 115 485
308. Luttinger J 1951 Phys. Rev. 84 814
309. Gerry C C and Singh V A 1979 Phys. Rev. D 20 2550
310. Yang C N and Mills R L 1954 Phys. Rev. 96 191
311. Goldman N, Kubasiak A, Gaspard P and Lewenstein M 2009 Phys. Rev. A 79 11
312. Barnett R, Boyd G R and Galitski V 2012 Phys. Rev. Lett. 109 235308
313. Horváthy P 1986 Phys. Rev. D 33 407
314. Gagel F and Maschke K 1995 Phys. Rev. B 52 2013
315. Kohmoto M 1989 Phys. Rev. B 39 11943-9
316. Hatsugai Y, Fukui T and Aoki H 2006 Phys. Rev. B 74 16
317. Lim L K, Hemmerich A and Morais Smith C 2010 Phys. Rev. A 81 023404
318. Wallace P R 1947 Phys. Rev. 71 622
319. Kimura T, Tamura H, Shiraishi K and Takayanagi H 2002 Phys. Rev. B 65 81307
320. Aoki H, Ando M and Matsumura H 1996 Phys. Rev. B 54 1517930
321. Vidal J, Mosseri R and Douçot B 1998 Phys. Rev. Lett. 81 5888
322. Goldman N, Urban D F and Bercioux D 2011 Phys. Rev. A 83 63601
323. Bercioux D, Goldman N and Urban D 2011 Phys. Rev. A 83 023609
324. Rammal R 1985 J. Phys. France 46 1345-54
325. Goerbig M 2011 Rev. Mod. Phys. 83 1193-243
326. Palmer R, Klein A and Jaksch D 2008 Phys. Rev. A 78 13
327. Powell S, Barnett R, Sensarma R and Das Sarma S 2010 Phys. Rev. Lett. 104 255303
328. Powell S, Barnett R, Sensarma R and Das Sarma S 2011 Phys. Rev. A 83 13612
329. Harper F, Simon S H and Roy R 2014 Phys. Rev. B 90 075104
330. Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
331. Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802
332. Bernevig B A and Zhang S C 2006 Phys. Rev. Lett. 96 106802
333. Bychkov Y A and Rashba E I 1984 J. Phys. C: Solid State Phys. 17 6039
334. Winkler R 2003 Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Berlin: Springer)
335. Fu L, Kane C L and Mele E J 2007 Phys. Rev. Lett. 98 106803
336. Goldman N, Satija I, Nikolic P, Bermudez A, Martin-Delgado M, Lewenstein M and Spielman I B 2010 Phys. Rev. Lett. 105 255302
337. Kennedy C J, Siviloglou G A, Miyake H, Burton W C and Ketterle W 2013 Phys. Rev. Lett. 111 225301
338. Cocks D, Orth P P, Rachel S, Buchhold M, Hur K L and Hofstetter W 2012 Phys. Rev. Lett. 109 205303
339. Orth P P, Cocks D, Rachel S, Buchhold M, Hur K L and Hofstetter W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134004
340. Goldman N, Kubasiak A, Bermudez A, Gaspard P, Lewenstein M and Martin-Delgado M A 2009 Phys. Rev. Lett. 103 35301
341. Zamora A, Szirmai G and Lewenstein M 2011 Phys. Rev. A 84 53620
342. Palmer R N and Pachos J K 2011 New J. Phys. 13 5002
343. Mei F, Zhu S L, Feng X L, Zhang Z M and Oh C 2011 Phys. Rev. A 84 023622
344. Graß T, Baranov M A and Lewenstein M 2011 Phys. Rev. A 84 43605
345. Komineas S and Cooper N R 2012 Phys. Rev. A 85 053623
346. Graß T, Saha K, Sengupta K and Lewenstein M 2011 Phys. Rev. A 84 53632
347. Vozmediano M A H, Katsnelson M I and Guinea F 2010 Phys. Rep. 496 109
348. Goldman N, Beugeling W and Morais Smith C 2012 Europhys. Lett. 97 23003
349. Satija I, Dakin D, Vaishnav J and Clark C 2008 Phys. Rev. A 77 043410
350. Goldman N and Gaspard P 2007 Europhys. Lett. 78 60001
351. Goldman N 2007 Europhys. Lett. 80 20001
352. Beugeling W, Goldman N and Morais Smith C 2012 Phys. Rev. B 86 075118
353. Maraner P and Pachos J K 2009 Phys. Lett. A 373 2542
354. Ruostekoski J, Dunne G V and Javanainen J 2002 Phys. Rev. Lett. 88 180401
355. Ruostekoski J, Javanainen J and Dunne G 2008 Phys. Rev. A 77 013603
356. Mueller E J 2004 Phys. Rev. A 70 041603
357. Kolovsky A R 2011 Europhys. Lett. 93 20003
358. Creffield C E and Sols F 2013 Europhys. Lett. 101 40001
359. Creffield C E and Sols F 2014 Phys. Rev. A 90 023636
360. Bermudez A, Schaetz T and Porras D 2011 Phys. Rev. Lett. 107 150501
361. Bermudez A, Schaetz T and Porras D 2012 New J. Phys. 14 05304
362. Anisimovas E, Gerbier F, Andrijauskas T and Goldman N 2014 Phys. Rev. A 89 013632
363. Goldman N, Gerbier F and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134010
364. Aidelsburger M, Atala M, Nascimbène S, Trotzky S, Chen Y A and Bloch I 2013 Appl. Phys. B (doi:10.1007/s00340-013-5418-1)
365. Mazza L, Bermudez A, Goldman N, Rizzi M, Martin-Delgado M A and Lewenstein M 2012 New J. Phys. 14 015007
366. Górecka A, Grémaud B and Miniatura C 2011 Phys. Rev. A 84 23604
367. Hemmerich A 2010 Phys. Rev. A 81 063626
368. Alba E, Fernandez-Gonzalvo X, Mur-Petit J, Pachos J and Garcia-Ripoll J 2011 Phys. Rev. Lett. 107 235301
369. Goldman N, Anisimovas E, Gerbier F, Öhberg P, Spielman I B and Juzeliunas G 2013 New J. Phys. 15 3025
370. Juzeliunas G and Spielman I B 2011 Physics 4 99
371. Sørensen A S, Demler E and Lukin M D 2005 Phys. Rev. Lett. 94 086803
372. Luttinger J M 1951 Phys. Rev. 84 814-7
373. Maricq M M 1982 Phys. Rev. B 25 6622-32
374. Rahav S, Gilary I and Fishman S 2003 Phys. Rev. A 68 013820
375. Grushin A G, Gomez-Leon A and Neupert T 2014 Phys. Rev. Lett. 112 156801
376. D'Alessio L and Polkovnikov A 2013 Ann. Phys. 333 19-33
377. Lazarides A, Das A and Moessner R 2014 Phys. Rev. Lett. 112 150401
378. Vorberg D, Wustmann W, Ketzmerick R and Eckardt A 2013 Phys. Rev. Lett. 111 240405
379. Langemeyer M and Holthaus M 2014 Phys. Rev. E 89 012101
380. Folman R, Kruger P, Schmiedmayer J, Denschlag J and Henkel C 2002 Adv. At. Mol. Opt. Phys. 48 263
381. Klein A and Jaksch D 2009 Europhys. Lett. 85 13001
382. Lang L J, Cai X and Chen S 2012 Phys. Rev. Lett. 108 220401
383. Mei F, Zhu S L, Zhang Z M, Oh C H and Goldman N 2012 Phys. Rev. A 85 13638
384. Aubry S and André G 1980 Ann. Israel Phys. Soc. 3 133
385. Roati G, D'Errico C, Fallani L, Fattori M, Fort C, Zaccanti M, Modugno G, Modugno M and Inguscio M 2008 Nature 453 895
386. Kraus Y E, Lahini Y, Ringel Z, Verbin M and Zilberberg O 2012 Phys. Rev. Lett. 109 106402
387. Deng X and Santos L 2014 Phys. Rev. A 89 033632
388. Kraus Y E, Ringel Z and Zilberberg O 2013 Phys. Rev. Lett. 111 226401
389. Boada O, Celi A, Latorre J I and Lewenstein M 2012 Phys. Rev. Lett. 108 133001
390. Celi A, Massignan P, Ruseckas J, Goldman N, Spielman I B, Juzeliunas G and Lewenstein M 2014 Phys. Rev. Lett. 112 043001
391. Hügel D and Paredes B 2014 Phys. Rev. A 89 023619
392. Atala M, Aidelsburger M, Lohse M, Barreiro J T, Paredes B and Bloch I 2013 Nature Phys. 10 588
393. Juliá-Díaz B, Grass T, Barberán N and Lewenstein M 2012 New J. Phys. 14 055003
394. Carusotto I and Ciuti C 2013 Rev. Mod. Phys. 85 299
395. Hafezi M, Demler E A, Lukin M D and Taylor J M 2011 Nature Phys. 7 907
396. Rechtsman M C, Zeuner J M, Plotnik Y, Lumer Y, Podolsky D, Dreisow F, Nolte S, Segev M and Szameit A 2013 Nature 496 196-200
397. Ozawa T and Carusotto I 2014 Phys. Rev. Lett. 112 133902
398. Hafezi M, Lukin M D and Taylor J M 2013 New J. Phys. 15 063001
399. Umucalilar R O and Carusotto I 2012 Phys. Rev. Lett. 108 206809
400. Umucalilar R O and Carusotto I 2013 Phys. Lett. A 377 2074
401. Haldane F and Raghu S 2008 Phys. Rev. Lett. 100 013904
402. Konig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L and Zhang S C 2007 Science 318 766-70
403. Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J and Hasan M Z 2008 Nature 452 970-4
404. Chen Y L et al 2009 Science 325 178
405. Jiang L, Kitagawa T, Alicea J, Akhmerov A, Pekker D, Refael G, Cirac J, Demler E, Lukin M and Zoller P 2011 Phys. Rev. Lett. 106 220402
406. Kraus C V, Diehl S, Zoller P and Baranov M A 2012 New J. Phys. 14 3036
407. Kraus C V, Dalmonte M, Baranov M A, Läuchli A M and Zoller P 2013 Phys. Rev. Lett. 111 173004
408. Nascimbène S 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134005
409. Atala M, Aidelsburger M, Barreiro J T, Abanin D, Kitagawa T, Demler E and Bloch I 2013 Nature Phys. 9 795
410. Zhang D w, Wang Z d and Zhu S l 2012 Front. Phys. 7 31-53
411. Bhat R, Peden B M, Seaman B T, Kramer M, Carr L D and Holland M J 2006 Phys. Rev. A 74 063606
412. Lim L K, Smith C M and Hemmerich A 2008 Phys. Rev. Lett. 100 130402
413. Goldbaum D S and Mueller E J 2009 Phys. Rev. A 79 21602
414. Zhai H, Umucallar R O and Oktel M Ö 2010 Phys. Rev. Lett. 104 145301
415. Brantut J P, Meineke J, Stadler D, Krinner S and Esslinger T 2012 Science 337 1069
416. Öhberg P, Juzeliunas G, Ruseckas J and Fleischhauer M 2005 Phys. Rev. A 72 053632
417. Hafezi M, Sorensen A S, Demler E and Lukin M D 2007 Phys. Rev. A 76 023613
418. Juliá-Díaz B, Dagnino D, Günter K J, Grass T, Barberán N, Lewenstein M and Dalibard J 2011 Phys. Rev. A 84 053605
419. Juliá-Díaz B, Grass T, Dutta O, Chang D E and Lewenstein M 2013 Nature Commun. 4 2046
420. Roncaglia M, Rizzi M and Dalibard J 2011 Sci. Rep. 1 43
421. Cooper N R, van Lankvelt F J M, Reijnders J W and Schoutens K 2005 Phys. Rev. A 72 63622
422. Bhat R, Kraemer M, Cooper J and Holland M J 2007 Phys. Rev. A 76 043601
423. Read N and Cooper N R 2003 Phys. Rev. A 68 35601
424. Graß T, Juliá-Díaz B and Lewenstein M 2012 Phys. Rev. A 86 053629
425. Shao L B, Zhu S L, Sheng L, Xing D Y and Wang Z D 2008 Phys. Rev. Lett. 101 246810
426. Stanescu T D, Galitski V, Vaishnav J Y, Clark C W and Das Sarma S 2009 Phys. Rev. A 79 53639
427. Li F, Sheng L and Xing D Y 2009 Europhys. Lett. 84 60004
428. Liu X J, Liu X, Wu C and Sinova J 2010 Phys. Rev. A 81 033622
429. Stanescu T D, Galitski V and Das Sarma S 2010 Phys. Rev. A 82 013608
430. Béri B and Cooper N 2011 Phys. Rev. Lett. 107 145301
431. Dauphin A, Müller M and Martin-Delgado M 2012 Phys. Rev. A 86 053618
432. Sun K, Liu W V, Hemmerich A and Das Sarma S 2012 Nature Phys. 8 67
433. Liu X J, Liu Z X and Cheng M 2013 Phys. Rev. Lett. 110 076401
434. Liu X J and Drummond P D 2012 Phys. Rev. A 86 035602
435. Kohmoto M 1985 Ann. Phys. 160 343
436. Thouless D J, Kohmoto M, Nightingale M P and den Nijs M 1982 Phys. Rev. Lett. 49 405-8
437. Ji Y, Chung Y, Sprinzak D, Heiblum M, Mahalu D and Shtrikman H 2003 Nature 422 415
438. Karmakar B et al 2011 Phys. Rev. Lett. 107 236804
439. Kundhikanjana W et al 2012 arXiv:1212.6441
440. Umucalilar R O, Zhai H and Oktel M Ö 2008 Phys. Rev. Lett. 100 70402
441. Streda P 1982 J. Phys. C: Solid State Phys. 15 L717
442. Bermudez A, Goldman N, Kubasiak A, Lewenstein M and Martin-Delgado M A 2010 New J. Phys. 12 033041
443. Zhao E, Bray-Ali N, Williams C, Spielman I B and Satija I 2011 Phys. Rev. A 84 063629
444. Price H and Cooper N 2012 Phys. Rev. A 85 033620
445. Dahan M B, Peik E, Reichel J, Castin Y and Salomon C 1996 Phys. Rev. Lett. 76 4508
446. Abanin D A, Kitagawa T, Bloch I and Demler E 2013 Phys. Rev. Lett. 110 165304
447. Liu X J, Law K T, Ng T K and Lee P A 2013 Phys. Rev. Lett. 111 120402
448. Dauphin A and Goldman N 2013 Phys. Rev. Lett. 111 135302
449. Wang L, Soluyanov A A and Troyer M 2013 Phys. Rev. Lett. 110 166802
450. King-Smith R D and Vanderbilt D 1993 Phys. Rev. B 47 1651
451. Goldman N, Beugnon J and Gerbier F 2013 Eur. Phys. J. 217 135
452. Goldman N, Dalibard J, Dauphin A, Gerbier F, Lewenstein M, Zoller P and Spielman I B 2013 Proc. Natl Acad. Sci. USA 110 1-11
453. Scarola V W and Das Sarma S 2007 Phys. Rev. Lett. 98 4
454. Goldman N, Beugnon J and Gerbier F 2012 Phys. Rev. Lett. 108 255303
455. Stenger J, Inouye S, Chikkatur A P, Stamper-Kurn D M, Pritchard D E and Ketterle W 1999 Phys. Rev. Lett. 82 4569
456. Killi M and Paramekanti A 2012 Phys. Rev. A 85 061606
457. Buchhold M, Cocks D and Hofstetter W 2012 Phys. Rev. A 85 63614
458. Javanainen J and Ruostekoski J 2003 Phys. Rev. Lett. 91 150404
459. Barnett R 2013 Phys. Rev. A 88 063631
460. Reichl M and Mueller E 2014 Phys. Rev. A 89 063628
461. Weitenberg C, Endres M, Sherson J F, Cheneau M, Schauß P, Fukuhara T, Bloch I and Kuhr S 2011 Nature 471 319-24
462. Wilczek F 1987 Phys. Rev. Lett. 58 1799
463. Fu L and Kane C L 2008 Phys. Rev. Lett. 100 96407
464. Alicea J 2010 Phys. Rev. B 81 125318
465. Alicea J, Oreg Y, Refael G, Oppen F V and Fisher M P A 2011 Nature Phys. 7 412
466. Zhu S L, Shao L B, Wang Z D and Duan L M 2011 Phys. Rev. Lett. 106 100404
467. Kraus C V, Zoller P and Baranov M A 2013 Phys. Rev. Lett. 111 203001
468. Pachos J K, Alba E, Lahtinen V and Garcia-Ripoll J J 2013 Phys. Rev. A 88 013622
469. Zohar E, Cirac J I and Reznik B 2012 Phys. Rev. Lett. 109 125302
470. Zohar E, Cirac J I and Reznik B 2013 Phys. Rev. Lett. 110 55302
471. Zohar E and Reznik B 2011 Phys. Rev. Lett. 107 275301
472. Keilmann T, Lanzmich S, McCulloch I and Roncaglia M 2011 Nature Commun. 2 361
473. Cirac J, Maraner P and Pachos J 2010 Phys. Rev. Lett. 105 190403
474. Zohar E, Cirac J I and Reznik B 2013 Phys. Rev. A 88 023617
475. Tewari S, Scarola V W, Senthil T and Das Sarma S 2006 Phys. Rev. Lett. 97 200401
476. Glaetzle A W, Dalmonte M, Nath R, Rousochatzakis I, Moessner R and Zoller P 2014 arXiv:1404.5326
477. Aglietti U, Griguolo L, Jackiw R, Pi S Y and Seminara D 1996 Phys. Rev. Lett. 77 4406-9
478. Edmonds M, Valiente M and Öhberg P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134013
479. Lee K L, Grémaud B, Han R, Englert B G and Miniatura C 2009 Phys. Rev. A 80 043411
480. Hou J M, Yang W X and Liu X J 2009 Phys. Rev. A 79 043621
481. Merkl M, Jacob A, Zimmer F E, Öhberg P and Santos L 2010 Phys. Rev. Lett. 104 073603
482. Kapit E and Mueller E 2011 Phys. Rev. A 83 33625
483. Kasamatsu K, Ichinose I and Matsui T 2013 Phys. Rev. Lett. 111 115303
484. Larson J and Levin S 2009 Phys. Rev. Lett. 103 013602
485. Larson J 2010 Phys. Rev. A 81 051803
486. Mivehvar F and Feder D L 2014 Phys. Rev. A 89 013803
487. Dong L, Zhou L, Wu B, Ramachandhran B and Pu H 2014 Phys. Rev. A 89 011602
488. Deng Y, Cheng J, Jing H and Yi S 2014 Phys. Rev. Lett. 112 143007
489. Boada O, Celi A, Latorre J I and Lewenstein M 2011 New J. Phys. 13 5002
490. Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D and Esslinger T 2014 arXiv:1406.7874
491. Parameswaran S A, Roy R and Sondhi S L 2003 C. R. Phys. 14 816
492. Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro T, Nascimbene S, Cooper N R, Bloch I and Goldman N arXiv:1407.4205
493. Roscilde T 2014 Phys. Rev. Lett. 112 110403
494. Duca L, Li T, Reitter M, Bloch I, Schleier-Smith M and Schneider U 2014 arXiv:1407.5635
495. Xiaoling Cui and Wei Yi 2014 Phys. Rev. X 4 031026
496. Zhe-Yu Shi, Xiaoling Cui and Hui Zhai 2014 Phys. Rev. Lett. 112 013201
497. Zygelman B 2013 J. Phys. B 46 134011
498. Kiffner M, Li W and Jaksch D 2013 Phys. Rev. Lett. 110 170402
499. Grusdt F and Fleischhauer M 2013 Phys. Rev. A 87 043628
500. Cesa A and Martin J 2013 Phys. Rev. A 88 062703
501. Olson A J, Wang S J, Niffenegger R J, Li C H, Greene C H and Chen Y P 2014 Phys. Rev. A 90 013616