Berry and Pancharatnam topological phases of atomic and optical systems

Journal of Optics B: Quantum and Semiclassical Optics

Volumn 6, Issue 4, 2004, Pages

  Ben Aryeh, Y ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Atomic and optical systems; Berry phases; Pancharatnam phases

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; FUNCTIONS; HAMILTONIANS; LIGHT POLARIZATION; PARAMETER ESTIMATION; PROBLEM SOLVING; QUANTUM THEORY; SPECTROSCOPIC ANALYSIS; THEOREM PROVING; TOPOLOGY;

ATOMIC AND OPTICAL SYSTEMS; BERRY PHASES; MONOPOLES; PANCHARATNAM PHASES;

OPTICAL SYSTEMS;

EID: 2342631309     PISSN: 14644266     EISSN: None     Source Type: Journal    
DOI: 10.1088/1464-4266/6/4/R01     Document Type: Review

References (201)

1. Aharonov Y and Bohm D 1959 Phys. Rev. 115 485
2. Herzberg G and Longuet-Higgins H C 1963 Discuss. Faraday Soc. 35 77
3. Mead C A and Truhlar D G 1979 J. Chem. Phys. 70 2284
4. Berry M V 1984 Proc. R. Soc. A 392 45
5. Eguchi T, Gilkey P B and Hanson A J 1980 Phys. Rep. 66 213
6. Frankel T 2001 The Geometry of Physics (Cambridge: Cambridge University Press)
7. Chern S S, Chen W H and Lam K S 1998 Lectures on Differential Geometry (Singapore: World Scientific)
8. Nakahara M 1989 Geometry, Topology and Physics (Bristol: Institute of Physics Publishing)
9. Nash C and Sen S 1983 Topology and Geometry for Physicists (London: Academic)
10. Simon B 1983 Phys. Rev. Lett. 51 2167
11. Aharonov Y and Anandan J 1987 Phys. Rev. Lett. 58 1593
12. Wilczek F and Zee A 1984 Phys. Rev. Lett. 52 2111
13. Yang C N and Mills R L 1954 Phys. Rev. 96 191
14. Hong-Mo C and Tsun T S 1993 Some Elementary Gauge Theory Concepts (Singapore: World Scientific)
15. Jackiw R 1988 Int. J. Mod. Phys. A 3 285
16. Gubarev F V and Zakharov V I 2002 Int. J. Mod. Phys. 17 157
17. Zanardi P and Rasetti M 1999 Phys. Lett. A 264 94
18. Pachos J, Zanardi P and Rasetti M 1999 Phys. Rev. A 61 010305
19. Pachos J and Chountasis S 2000 Phys. Rev. A 62 052318
20. Pachos J and Zanardi P 2001 J. Mod. Phys. B 15 1257
21. Margolin A E, Strazhev V I and Tregubovich A Y 2002 Phys. Lett. A 303 131
22. Margolin A E, Strazhev V I and Tregubovich A Y 2003 Phys. Lett. A 312 296
23. Hannay J H 1985 J. Phys. A: Math. Gen. 18 221
24. Berry M V 1985 J. Phys. A: Math. Gen. 18 15
25. Pati A K 1998 Ann. Phys. 270 178
26. Cerveró J M and Lejarreta D 1990 Quantum Opt. 2 333
27. Anandan J and Aharonov Y 1988 Phys. Rev. D 38 1863
28. Anandan J and Stodolsky L 1987 Phys. Rev. D 35 2597
29. Jordan T F 1987 J. Math. Phys. 28 1759
30. Chiao R Y and Wu Y 1986 Phys. Rev. Lett. 57 933
31. Tomita A and Chiao R Y 1986 Phys. Rev. Lett. 57 937
32. Pancharatnam S 1956 Proc. Ind. Acad. Sci. A 44 247
33. Sjoqvist E 2001 Phys. Rev. A 63 035602
34. Jordan T F 1988 Phys. Rev. A 38 1590
35. Samuel J and Bhandari R 1988 Phys. Rev. Lett. 60 2339
36. Mukunda N and Simon R 1993 Ann. Phys. 228 205
37. Aitchison I J R and Wanelik K 1992 Proc. R. Soc. 439 25
38. Pati A K 1995 Phys. Rev. A 52 2576
39. Bhandari R and Samuel J 1988 Phys. Rev. Lett. 60 1211
40. Bhandari R 1988 Phys. Lett. A 133 1 Bhandari R 1990 Phys. Lett. A 143 170 Bhandari R 1991 Phys. Lett. A 157 221 Bhandari R 1992 Phys. Lett. A 171 262 Bhandari R 1993 Phys. Lett. A 180 15
41. Bhandari R 1988 Phys. Lett. A 133 1 Bhandari R 1990 Phys. Lett. A 143 170 Bhandari R 1991 Phys. Lett. A 157 221 Bhandari R 1992 Phys. Lett. A 171 262 Bhandari R 1993 Phys. Lett. A 180 15
42. Bhandari R 1988 Phys. Lett. A 133 1 Bhandari R 1990 Phys. Lett. A 143 170 Bhandari R 1991 Phys. Lett. A 157 221 Bhandari R 1992 Phys. Lett. A 171 262 Bhandari R 1993 Phys. Lett. A 180 15
43. Bhandari R 1988 Phys. Lett. A 133 1 Bhandari R 1990 Phys. Lett. A 143 170 Bhandari R 1991 Phys. Lett. A 157 221 Bhandari R 1992 Phys. Lett. A 171 262 Bhandari R 1993 Phys. Lett. A 180 15
44. Bhandari R 1988 Phys. Lett. A 133 1 Bhandari R 1990 Phys. Lett. A 143 170 Bhandari R 1991 Phys. Lett. A 157 221 Bhandari R 1992 Phys. Lett. A 171 262 Bhandari R 1993 Phys. Lett. A 180 15
45. Bhandari R 1997 Phys. Rep. 281 1
46. Bitter T and Dubbers D 1987 Phys. Rev. Lett. 59 251
47. Suter D, Mueller K T and Pines A 1988 Phys. Rev. Lett. 60 1218
48. Simon R, Kimble H J and Sudarshan E C G 1988 Phys. Rev. Lett. 61 19
49. Agarwal G S 1991 Opt. Commun. 82 213
50. Chiao R Y and Jordan T F 1988 Phys. Lett. A 132 77
51. Kitano M and Yabuzaki T 1989 Phys. Lett. A 142 321
52. Hariharan P, Roy M, Robinson P A and O'Byrne J W 1993 J. Mod. Opt. 40 871
53. Kwiat P G and Chiao R Y 1991 Phys. Rev. Lett. 66 588
54. Brendel J, Dultz W and Martienssen W 1995 Phys. Rev. A 52 2551
55. Grayson T P, Torgerson J R and Barbosa G A 1994 Phys. Rev. A 49 626
56. Frins E M and Dultz W 1997 Opt. Commun. 136 354
57. Senthilkumaran P, Culshaw B and Thursby G 2000 J. Opt. Soc. Am. B 17 1914
58. Rauch H and Werner S A 2000 Neutron Interferometry (Oxford: Clarendon)
59. Wagh A G and Rakhecha V C 1990 Phys. Lett. A 146 369 Wagh A G and Rakhecha V C 1992 Phys. Lett. A 170 71 Wagh A G and Rakhecha V C 1995 Phys. Lett. A 197 107
60. Wagh A G and Rakhecha V C 1990 Phys. Lett. A 146 369 Wagh A G and Rakhecha V C 1992 Phys. Lett. A 170 71 Wagh A G and Rakhecha V C 1995 Phys. Lett. A 197 107
61. Wagh A G and Rakhecha V C 1990 Phys. Lett. A 146 369 Wagh A G and Rakhecha V C 1992 Phys. Lett. A 170 71 Wagh A G and Rakhecha V C 1995 Phys. Lett. A 197 107
62. Wagh A G, Rakhecha V C, Fischer P and Joffe A 1998 Phys. Rev. Lett. 81 1992
63. Wagh A G, Rakhecha V C, Summhammer J, Badurek G, Weinfurter H, Allman B E, Kaiser H, Harnacher K, Jacobson D L and Werner S A 1997 Phys. Rev. Lett. 78 755
64. Sanders B C, De Guise H, Bartlett S D and Zhang W 2001 Phys. Rev. Lett. 86 369
65. Strahov E 2001 J. Math. Phys. 42 2008
66. Ben-Aryeh Y 2002 J. Mod. Opt. 49 207
67. Ben-Aryeh Y 2003 Opt. Spectrosc. 94 783
68. Tong D M, Kwek L C and Oh C H 2003 J. Phys. A: Math. Gen. 36 1149
69. Tong D M, Sjoqvist E, Kwek L C, Oh C H and Ericsson M 2003 Phys. Rev. A 68 022106
70. Hessmo B and Sjöqvist E 2000 Phys. Rev. A 62 062301
71. Milman P and Mosseri R 2003 Phys. Rev. Lett. 90 230403
72. Sjöqvist E 2000 Phys. Rev. A 62 022109
73. Sjöqvist E, Pati A K, Ekert A, Anandan J S, Ericsson M, Oi D K L and Vedral V 2000 Phys. Rev. Lett. 85 2845
74. Singh K, Tong D M, Basu K, Chen J L and Du J F 2003 Phys. Rev. A 67 032106
75. Du J F, Zhou P, Shi M, Kwek L C, Pan J-W, Oh C H, Ekert A, Oi D K L and Ericsson M 2003 Phys. Rev. Lett. 91 100403
76. Ericsson M, Sjöqvist E, Brännlund J, Oi D K L and Pati A K 2003 Phys. Rev. A 67 020101
77. Filipp S and Sjoqvist E 2003 Phys. Rev. Lett. 90 050403
78. Nazir A, Spiller T P and Munro W J 2002 Phys. Rev. A 65 042303
79. Friedenauer A and Sjöqvist E 2003 Phys. Rev. A 67 024303
80. Jones J A, Vedral V, Ekert A and Castagnoli G 2000 Nature 403 869
81. Shapere A and Wilczek F 1989 Geometric Phases in Physics (Singapore: World Scientific)
82. Yoshioka D 2002 The Quantum Hall Effect (Berlin: Springer)
83. Anandan J and Aharonov Y 1990 Phys. Rev. Lett. 65 1697
84. Provost J P and Vallee G 1980 Commun. Math. Phys. 76 289
85. Pati A K and Joshi A 1993 Europhys. Lett. 21 723
86. Abe S 1993 Phys. Rev. A 48 4102
87. Berry M V 1989 (page 7, in [75])
88. Dattoli G, Dipace A and Torre A 1986 Phys. Rev. A 33 4387
89. Bohm A, Boya L J and Kendrick B 1991 Phys. Rev. A 43 1206
90. Dirac A M 1931 Proc. R. Soc. A 133 60
91. Jackson J D 1975 Classical Electrodynamics (New York: Wiley)
92. Goddard P and Olive D 1978 Rep. Prog. Phys. 41 1357
93. Wu T and Yang C N 1976 Nucl. Phys. B 107 365
94. Jackiw R 1980 Ann. Phys. 129 183
95. Cirelli R and Lanzavecchia P 1984 Nuovo Cimento 79 271
96. Cirelli R, Mania A and Pizzocchero L 1991 Int. J. Mod. Phys. 6 2133
97. Flaherty E J 1976 Hermitian and Kählerian Geometry in Relativity (Springer Lecture Notes in Physics) (Berlin: Springer)
98. Page D N 1987 Phys. Rev. A 36 3479
99. de Polaviega G G and Sjöqvist E 1998 Am. J. Phys. 66 431
100. Mead C A 1992 Rev. Mod. Phys. 64 51
101. Longuet-Higgins H C 1975 Proc. R. Soc. A 344 147
102. Mead C A 1979 J. Chem. Phys. 70 2276
103. Mead C A 1987 Phys. Rev. Lett. 59 161
104. Sjoqvist E and Hedström M 1997 Phys. Rev. A 56 3417
105. Sjoqvist E 2002 Phys. Rev. Lett. 89 210401
106. Avron J E 2000 Phys. Rev. A 62 062504
107. Aitchison I J R 1988 Phys. Scr. T 23 12
108. Sakurai J J 1994 Modern Quantum Mechanics (New York: Addison-Wesley)
109. Kuratsuji H and Ida S 1985 Prog. Theor. Phys. 74 439
110. von Busch H, Dev V, Eckel H-A, Kasahara S, Wang J, Demtröder W, Sebald P and Meyer W 1998 Phys. Rev. Lett. 81 4584
111. Born M and Wolf E 1965 Principles of Optics (Oxford: Pergamon)
112. Yariv A 1991 Optical Electronics (New York: Saunders)
113. Chyba T H, Wang L J, Mandel L and Simon R 1988 Opt. Lett. 13 562
114. Berry M V 1987 Nature 326 277
115. Lipson S G 1990 Opt. Lett. 15 154
116. Ross J N 1984 Opt. Quantum Electron. 16 455
117. Haldane F D M 1987 Phys. Rev. Lett. 59 1788
118. Shen J-Q and Ma L-H 2003 Phys. Lett. A 308 355
119. Chiao R Y, Antaramian A, Ganga K M, Jiao H, Wilkinson S R and Nathel H 1988 Phys. Rev. Lett. 60 1214
120. Jiao H, Wilkinson S R, Chiao R Y and Nathel H 1989 Phys. Rev. A 39 3475
121. Siebert K J, Schmitzer H and Dultz W 2002 Phys. Lett. A 300 341
122. Jordan T F 1988 Phys. Rev. Lett. 60 1584
123. Klein A G and Werner S A 1983 Rep. Prog. Phys. 46 259
124. Rauch H, Zeilinger A, Badurek G, Wilfing A, Bauspiess W and Bonse U 1975 Phys. Lett. 54 425
125. Klein A G and Opat G I 1976 Phys. Rev. Lett. 37 238
126. Mezei F 1988 Physica B 151 74
127. Badurek G, Rauch H, Zeilinger A, Bauspiess W and Bonse A 1976 Phys. Rev. D 14 1177
128. Summhammer J, Budarek G, Rauch H, Kischko U and Zeilinger A 1983 Phys. Rev. A 27 2523
129. Werner S A, Colella R, Overhauser A W and Eagen C F 1975 Phys. Rev. Lett. 35 1053
130. Aharonov Y and Susskind L 1967 Phys. Rev. 158 1237
131. Manini N and Pistolesi F 2000 Phys. Rev. Lett. 85 3067
132. Hasegawa Y, Loidl R, Baron M, Badurek G and Rauch H 2002 Phys. Rev. Lett. 87 070401
133. Hasegawa Y, Loidl R, Badurek G, Baron M, Manini N, Pistolesi F and Rauch H 2002 Phys. Rev. A 65 052111
134. Hasegawa Y, Zawisky M, Rauch H and Joffe A I 1996 Phys. Rev. A 53 2486
135. Gerry C C 1989 Phys. Rev. A 39 3204
136. Cerveró J M and Lejarreta J D 1998 J. Phys. A: Math. Gen. 31 5507
137. Cerveró J M and Lejarreta J D 1997 Quantum Semiclass. Opt. 9 L5
138. Swensmark H and Dimon P 1994 Phys. Rev. Lett. 73 3387
139. Berry M V 1987 J. Mod. Opt. 34 1401
140. Ben-Aryeh Y 2003 J. Mod. Opt. 50 2791
141. Giller S, Kosinski P and Szymanowski L 1989 Int. J. Mod. Phys. A 4 1453
142. Bouchiat C 1989 J. Physique 50 1041
143. Joshi A, Pati A K and Banerjee A 1994 Phys. Rev. A 49 5131
144. Khanna G, Mukhopadhyay S, Simon R and Mukunda N 1997 Ann. Phys. 253 55
145. Bukanov I V, Tolkachev E A and Tregubovich A Y 1996 Phys. At. Nucl. 59 659
146. Arvind, Mallesh K S and Mukunda N 1997 J. Phys. A: Math. Gen. 30 2417
147. Cheng C M and Fung P C W 1989 J. Phys. A: Math. Gen. 22 3493
148. Chaturvedi S, Sriram M S and Srinivasan V 1987 J. Phys. A: Math. Gen. 20 L1071
149. Seshadri S, Lakshmibala S and Balakrishnan V 1997 Phys. Rev. A 55 869
150. Bouchiat C and Gibbons G W 1988 J. Physique 49 187
151. Olshani M A 1994 Phys. Lett. A 186 369
152. Lawande Q V, Lawande S V and Joshi A 1999 Phys. Lett. A 251 164
153. Moore D J and Stedman G E 1990 J. Phys. A: Math. Gen. 23 2049
154. Reich M, Sterr U and Ertmer W 1993 Phys. Rev. A 47 2518
155. Ellinas D, Barnett S M and Dupertuis M A 1989 Phys. Rev. A 39 3228
156. Ortega R and Santander M 2003 J. Phys. A: Math. Gen. 36 459
157. Abdel-Aty M 2003 J. Opt. B: Quantum Semiclass. Opt. 5 349
158. Giavarini G and Onofri E 1989 J. Math. Phys. 30 659
159. Klyshko D N 1989 Phys. Lett. A 140 19
160. Wang X-B, Kwek L C and Oh C H 2000 Phys. Rev. A 62 032105
161. Liang M-L and Wu H-B 2003 Phys. Scr. T 68 41
162. Maamache M and Bekkar H 2003 J. Phys. A: Math. Gen. 36 L359
163. Moore D J 1992 Quantum Opt. 4 123
164. Bose S, Carrolo A, Fuentes-Guridi I, Santos M F and Vedral V 2003 J. Mod. Opt. 50 1175
165. Wang X-B and Keiji M 2001 Phys. Rev. Lett. 87 097901
166. Fuentes-Guridi I, Bose S and Vedral V 2000 Phys. Rev. Lett. 85 5018
167. Ge Y C and Child M S 1997 Phys. Rev. Lett. 78 2507
168. Asorey M, Carinena J F and Paramio M 1982 J. Math. Phys. 23 1451
169. Wu Y-S and Li H-Z 1988 Phys. Rev. B 38 11907
170. Pati A K 1992 J. Phys. A: Math. Gen. 25 L1001
171. Pati A K 1999 Phys. Rev. A 60 121
172. Cen L, Li X, Yan Y, Zheng H and Wang S 2003 Phys. Rev. Lett. 90 147902
173. Yang L and Yan F 2000 Phys. Lett. A 265 326
174. Anandan J 1990 Phys. Lett. A 147 3
175. Bohm A, Boya L J, Mostafazadeh A and Rudolph G 1993 J. Geom. Phys. 12 13
176. Sjöqvist E 2001 Phys. Lett. A 286 4
177. Kiritsis E 1987 Commun. Math. Phys. 111 417
178. Boya L J, Perelomov A M and Santander M 2001 J. Math. Phys. 42 5130
179. Jordan T F 1988 J. Math. Phys. 29 2042
180. Pati A K 2003 Int. J. Quantum Inf. 1 135
181. Tidstrom J and Sjöqvist E 2003 Phys. Rev. A 67 032110
182. Larsson P and Sjöqvist E 2003 Phys. Lett. A 315 12
183. Pati A K 1991 Phys. Lett. A 159 105
184. Segert J 1987 J. Math. Phys. 28 2102
185. Andreev A V, Klimov A B and Lerner P B 1990 Europhys. Lett. 12 101
186. Moore D J 1990 J. Phys. A: Math. Gen. 23 L665
187. Byrd M 1998 J. Math. Phys. 39 6125
188. Segev M, Solomon R and Yariv A 1992 Phys. Rev. Lett. 69 590
189. Tian M, Reibel R R, Barber Z B, Fischer J A and Babbit W R 2003 Phys. Rev. A 67 011403(R)
190. Weinfurther H and Badurek G 1990 Phys. Rev. Lett. 64 1318
191. Tycko R 1987 Phys. Rev. Lett. 58 2281
192. Webb C L, Godun R M, Summy G S, Oberthaler M K, Featonby P D, Foot C J and Burnett K 1999 Phys. Rev. A 60 R1783
193. Richardson D J, Kilvington A I, Green K and Lamoreaux S K 1988 Phys. Rev. Lett. 61 2030
194. Tompkin W R, Malcuit M S, Boyd R W and Chiao R Y 1990 J. Opt. Soc. Am. B 7 230
195. Vedral V 2003 Int. J. Quantum Inf. 1 1
196. Pistolesi F and Manini N 2000 Phys. Rev. Lett. 85 1585
197. Mostafazadeh A 1997 Phys. Rev. A 55 1653
198. Samuel J and Dhar A 2001 Phys. Rev. Lett. 87 260401
199. Lauber H-M, Weidenhammer P and Dubbers D 1994 Phys. Rev. Lett. 72 1004
200. Manolopoulos D E and Child M S 1999 Phys. Rev. Lett. 82 2223
201. Falci G, Fazio R, Palma G M, Siewert J and Vedral V 2000 Nature 407 355