Theoretical progress in many-body physics with ultracold dipolar gases

Physics Reports

Volumn 464, Issue 3, 2008, Pages 71-111

  Baranov, M A ^a,b,c  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^c KURCHATOV INSTITUTE   (Russian Federation)

Author keywords

BCS pairing; Bose Einstein condensation; Dipole dipole interaction; Trapped gas

Indexed keywords

EID: 48949115559     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2008.04.007     Document Type: Review

References (166)

1. Griesmaier A., Werner J., Hensler S., Stuhler J., and Pfau T. Bose-Einstein condensation of chromium. Phys. Rev. Lett. 94 (2005) 160401
2. Stuhler J., Griesmaier A., Koch T., Fattori M., Pfau T., Giovanazzi S., Pedri P., and Santos L. Observation of dipole-dipole interaction in a degenerate quantum gas. Phys. Rev. Lett. 95 (2005) 150406
3. Fattori M., Koch T., Goetz S., Griesmaier A., Hensler S., Stuhler J., and Pfau T. Demagnetization cooling of a gas. Nature Phys. 2 (2006) 765
4. Griesmaier A., Stuhler J., Koch T., Fattori M., Pfau T., and Giovanazzi S. Comparing contact and dipolar interaction in a Bose-Einstein condensate. Phys. Rev. Lett. 97 (2006) 250402
5. Lahaye T., Koch T., Fröhlich B., Fattori M., Metz J., Griesmaier A., Giovanazzi S., and Pfau T. Strong dipolar effects in a quantum ferrofluid. Nature 448 (2007) 672
6. Koch T., Lahaye T., Metz J., Fröhlich B., Griesmaier A., and Pfau T. Stabilization of a purely dipolar quantum gas against collapse. Nature Phys. 4 (2008) 218
7. T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister, A. Griesmaier, T. Pfau, H. Saito, Y. Kawaguchi, M. Ueda, d-wave collapse and explosion of a dipolar Bose-Einstein condensate. cond-mat arXiv:0803.2442, 2008
8. Weinstein J.D., deCarvalho R., Guillet T., Friedrich B., and Doyle J.M. Magnetic trapping of calcium monohydride molecules at millikelvin temperatur. Nature (London) 395 (1998) 148
9. Doyle J.M., and Friedrich B. Molecules are cool. Nature (London) 401 (1999) 749
10. Bethlem H.L., Berden G., and Meijer G. Decelerating neutral dipolar molecules. Phys. Rev. Lett. 83 (1999) 1558
11. Bethlem H.L., Berden G., van Roij A.J.A., Crompvoets F.M.H., and Meijer G. Trapping neutral molecules in a traveling potential well. Phys. Rev. Lett. 84 (2000) 5744
12. Bethlem H.L., Berden G., Crompvoets F.M.H., Jongma R.T., van Roij A.J.A., and Meijer G. Electrostatic trapping of ammonia molecules. Nature (London) 406 (2000) 491
13. Bethlem H.L., Crompvoets F.M.H., Jongma R.T., van de Meerakker S.Y.T., and Meijer G. Deceleration and trapping of ammonia using time-varying electric fields. Phys. Rev. A 65 (2002) 053416
14. In: Doyle J., Friedrich B., Krems R.V., and Masnou-Seeuws F. (Eds). Ultracold Polar Molecules: Formation and Collisions. Eur. Phys. J. D 31 2 (2004) (special issue)
15. van de Meerakker S.Y.T., Smeets P.H.M., Vanhaecke N., Jongma R.T., and Meijer G. Deceleration and electrostatic trapping of OH radicals. Phys. Rev. Lett. 94 (2005) 023004
16. Bochinski J.R., Hudson E.R., Lewandowski H.J., and Ye J. Cold free-radical molecules in the laboratory frame. Phys. Rev. A 70 (2004) 043410
17. 85Rb. Eur. Phys. J. D 31 (2004) 165
18. Egorov D., Campbell W.C., Friedrich B., Maxwell S.E., Tsikata E., van Buuren L.D., and Doyle J.M. Buffer-gas cooling of NH via the beam loaded buffer-gas method. Eur. Phys. J. D 31 (2004) 307
19. Sage J.M., Sainis S., Bergeman T., and DeMille D. Phys. Rev. Lett. 94 (2005) 203001
20. Marinescu M., and You L. Controlling atom-atom interaction at ultralow temperatures by dc electric fields. Phys. Rev. Lett. 81 (1998) 4596
21. Santos L., Shlyapnikov G.V., Zoller P., and Lewenstein M. Bose-Einstein condensation in trapped dipolar gases. Phys. Rev. Lett. 85 (2000) 1791
22. Jaksch D., Cirac J.I., Zoller P., Rolston S.L., Côté R., and Lukin M.D. Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85 (2000) 2208
23. Brennen G.K., Caves C.M., Jessen P.S., and Deutsch I.H. Quantum logic gates in optical lattices. Phys. Rev. Lett. 82 (1999) 1060
24. DeMille D. Quantum computation with trapped polar molecules. Phys. Rev. Lett. 88 (2002) 067901
25. Rabl P., DeMille D., Doyle J.M., Lukin M.D., Schoelkopf R.J., and Zoller P. Hybrid quantum processors: Molecular ensembles as quantum memory for solid state circuits. Phys. Rev. Lett. 97 (2006) 033003
26. Landau L.D., and Lifshitz E.M. Quantum Mechanics (1999), Butterworth-Heinemann, Oxford
27. Deb B., and You L. Low-energy atomic collision with dipole interactions. Phys. Rev. A 64 (2001) 022717
28. Kagan Yu., Vartanyants I.A., and Shlyapnikov G.V. Kinetics of decay of metastable gas phase of polarized atomic hydrogen at low temperatures. Sov. Phys. JETP 54 (1981) 590
29. Koelman J.M.V.A., Stoof H.T.C., Verhaar B.J., and Walraven J.T.M. Spin-polarized deuterium in magnetic traps. Phys. Rev. Lett. 59 (1987) 676
30. Koelman J.M.V.A., Stoof H.T.C., Verhaar B.J., and Walraven J.T.M. Lifetime of magnetically trapped ultracold atomic deuterium gas. Phys. Rev. B 38 (1988) 9319
31. Walraven J.T.M. In: Dalgarno A., et al. (Ed). Sixteenth International Conference on the Physics of Electronic and Atomic Collisions. AIP Conf. Proc. vol. 205 (1990), AIP, New York
32. Shlyapnikov G.V., Walraven J.T.M., Rahmanov U.M., and Reynolds M.W. Decay kinetics and bose condensation in a gas of spin-polarized triplet Helium. Phys. Rev. Lett. 73 (1994) 3247
33. You L., and Marinescu M. Prospects for p-wave paired Bardeen-Cooper-Schriffer states for fermionic atoms. Phys. Rev. A 60 (2000) 2324
34. Ticknor C., and Bohn J.L. Long-range scattering resonances in strong-field-seeking states of polar molecules. Phys. Rev. A 72 (2005) 032717
35. Yi S., and You L. Trapped atomic condensates with anisotropic interactions. Phys. Rev. A 61 (2000) 041604
36. Yi S., and You L. Trapped condensates of atoms with dipole interactions. Phys. Rev. A 63 (2001) 053607
37. Bortolotti D.C.E., Ronen S., Bohn J.L., and Blume D. Scattering length instability in dipolar Bose-Einstein condensates. Phys. Rev. Lett. 97 (2006) 160402
38. Ronen S., Bortolotti D.C.E., Blume D., and Bohn J.L. Dipolar Bose-Einstein condensates with dipole-dependent scattering length. Phys. Rev. A 74 (2006) 033611
39. Derevianko A. Anisotropic pseudopotential for polarized dilute quantum gases. Phys. Rev. A 67 (2003) 033607
40. Derevianko A. Erratum: Anisotropic pseudopotential for polarized dilute quantum gases [Phys. Rev. A 67 (2003) 033607]. Phys. Rev. A 72 (2005) 03990
41. Giovanazzi S., Görlitz A., and Pfau T. Tuning the dipolar interaction in quantum gases. Phys. Rev. Lett. 89 (2002) 130401
42. Dalfovo F., Giorgini S., Pitaevskii L.P., and Stringari S. Theory of Bose-Einstein condensation in trapped gases. Rev. Modern Phys. 71 (1999) 463
43. Santos L., Shlyapnikov G.V., Zoller P., and Lewenstein M. Bose-Einstein condensation in trapped dipolar gases. Phys. Rev. Lett. 85 (2000) 1791
44. Lushnikov P.M. Collapse of Bose-Einstein condensates with dipole-dipole interactions. Phys. Rev. A 66 (2002) 051601R
45. Santos L., Shlyapnikov G.V., Zoller P., and Lewenstein M. Erratum: Bose-Einstein condensation in trapped dipolar gases [Phys. Rev. Lett. 85 (2000) 1791]. Phys. Rev. Lett. 88 (2002) 139904
46. Ronen S., Bortolotti D.C.E., and Bohn J.L. Radial and angular rotons in trapped dipolar gases. Phys. Rev. Lett. 98 (2007) 030406
47. Dutta O., and Meystre P. Ground-state structure and stability of dipolar condensates in anisotropic traps. Phys. Rev. A 75 (2007) 053604
48. Eberlein C., Giovanazzi S., and O'Dell D.H.J. Exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions. Phys. Rev. A 71 (2005) 033618
49. Góral K., Rzażewski K., and Pfau T. Bose-Einstein condensation with magnetic dipole-dipole forces. Phys. Rev. A 61 (2000) 051601(R)
50. Martikainen J.P., Mackie M., and Suominen K.-A. Comment on "Bose-Einstein condensation with magnetic dipole-dipole forces". Phys. Rev. A 64 (2001) 037601
51. Santos L., Shlyapnikov G.V., and Lewenstein M. Roton-Maxon spectrum and stability of trapped dipolar Bose-Einstein condensates. Phys. Rev. Lett. 90 (2003) 250403
52. Ruprecht P.A., Edwards M., Burnett K., and Clark C.W. Probing the linear and nonlinear excitations of Bose-condensed neutral atoms in a trap. Phys. Rev. A 54 (1996) 4178
53. Góral K., and Santos L. Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gases. Phys. Rev. A 66 (2002) 023613
54. O'Dell D.H.J., Giovanazzi S., and Eberlein C. Exact hydrodynamics of a trapped dipolar Bose-Einstein condensate. Phys. Rev. Lett. 92 (2004) 250401
55. Baranov M., Dobrek Ł., Góral K., Santos L., and Lewenstein M. Ultracold dipolar gases - a challenge for experiments and theory. Phys. Scri. T102 (2002) 74
56. Fischer U.R. Stability of quasi-two-dimensional Bose-Einstein condensates with dominant dipole-dipole interactions. Phys. Rev. A 73 (2006) 031602R
57. Stringari S. Dynamics of Bose-Einstein condensed gases in highly deformed traps. Phys. Rev. A 58 (1998) 2385
58. Litvak A.G., Mironov V.A., Fraiman G.M., and Yunakovskii A.D. Thermal self-effect of wave beams in a plasma with a nonlocal nonlinearity. Sov. J. Plasma Phys. 1 (1975) 31
59. Peccianti M., Conti C., Assanto G., De Luca A., and Umeton C. Routing of anisotropic spatial solitons and modulational instability in liquid crystals. Nature (London) 432 (2004) 733
60. Krolikowski W., Bang O., Rasmussen J.J., and Wyller J. Modulational instability in nonlocal nonlinear Kerr media. Phys. Rev. E 64 (2001) 016612
61. Bang O., Krolikowski W., Wyller J., and Rasmussen J.J. Collapse arrest and soliton stabilization in nonlocal nonlinear media. Phys. Rev. E 66 (2002) 046619
62. Yakimenko A.I., Zaliznyak Y.A., and Kivshar Y. Stable vortex solitons in nonlocal self-focusing nonlinear media. Phys. Rev. E 71 (2005) 065603
63. Rosanov N.N., Rozhdestvenskii Yu.V., Smirnov V.A., and Fedorov S.V. Atomic "needles"and "bullets" in Bose-Einstein condensate and the formation of nanosized structures. JETP Lett. 77 (2003) 84
64. Shih M.-f., Segev M., and Salamo G. Three-dimensional spiraling of interacting spatial solitons. Phys. Rev. Lett. 78 (1997) 2551
65. Pedri P., and Santos L. Two-dimensional bright solitons in dipolar Bose-Einstein condensates. Phys. Rev. Lett. 95 (2005) 200404
66. Zakharov V.E., and Shabat A.B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Zh. Eksp. Teor. Fiz. 61 (1971) 118
67. Zakharov V.E., and Shabat A.B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34 (1972) 62
68. Zakharov V.E., and Shabat A.B. Interaction between solitons in a stable medium. Zh. Eksp. Teor. Fiz. 64 (1973) 1627
69. Zakharov V.E., and Shabat A.B. Interaction between solitons in a stable medium. Sov. Phys. JETP 37 (1973) 823
70. Nath R., Pedri P., and Santos L. Soliton-soliton scattering in dipolar Bose-Einstein condensates. Phys. Rev. A 76 (2007) 013606
71. Kalia R.K., and Vashishta P. Interfacial colloidal crystals and melting transition. J. Phys. C. 14 (1981) L643
72. Büchler H.P., Demler E., Lukin M., Micheli A., Prokof'ev N., Pupillo G., and Zoller P. Strongly correlated 2d quantum phases with cold polar molecules: Controlling the shape of the interaction potential. Phys. Rev. Lett. 98 (2007) 060404
73. Astrakharchik G.E., Boronat J., Kurbakov I.L., and Lozovik Yu.E. Quantum phase transition in a two-dimensional system of dipoles. Phys. Rev. Lett. 98 (2007) 060405
74. Fisher M.P.A., Weichman P.B., Grinstein G., and Fisher D.S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40 (1989) 546
75. Jaksch D., Bruder C., Cirac J.I., Gardiner C.W., and Zoller P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81 (1998) 3108
76. Greiner M., Mandel O., Esslinger T., Hänsch T.W., and Bloch I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature (London) 415 (2002) 39
77. Bruder C., Fazio R., and Schön G. Superconductor-Mott-insulator transition in Bose systems with finite-range interactions. Phys. Rev. B 47 (1993) 342
78. van Otterlo A., and Wagenblast K.-H. Coexistence of diagonal and off-diagonal long-range order: A Monte Carlo study. Phys. Rev. Lett. 72 (1994) 3598
79. Batrouni G.G., Scalettar R.T., Zimanyi G.T., and Kampf A.P. Supersolids in the Bose-Hubbard Hamiltonian. Phys. Rev. Lett. 74 (1995) 2527
80. Kühner T.D., White S.R., and Monien H. One-dimensional Bose-Hubbard model with nearest-neighbor interaction. Phys. Rev. B 61 (2000) 12474
81. Andreev A.F., and Lifshitz I.M. Quantum theory of crystal defects. Sov. Phys. JETP 29 (1969) 1107
82. Chester G.V. Speculations on Bose-Einstein condensation and quantum crystals. Phys. Rev. A 2 (1970) 256
83. Leggett A.J. Can a solid be "superfluid"?. Phys. Rev. Lett. 25 (1970) 1543
84. Kim E., and Chan M.H.W. Probable observation of a supersolid helium phase. Nature 427 (2004) 225
85. Kim E., and Chan M.H.W. Observation of superflow in solid helium. Science 305 (2004) 1941
86. Sasaki S., Ishiguro R., Caupin F., Maris H.J., and Balibar S. Superfluidity of grain boundaries and supersolid behavior. Science 313 (2006) 1098
87. Lin X., Clark A.C., and Ch M.H.W. an, Probable heat capacity signature of the supersolid transition. Nature 449 (2007) 1025
88. S. Sasaki, F. Caupin, S. Balibar, Wetting properties of grain boundaries in solid helium 4, arXiv:0707.3110v3[cond-mat.other]
89. Das D., and Doniach S. Existence of a Bose metal at T = 0. Phys. Rev. B 60 (1999) 1261
90. Dalidovich D., and Phillips P. Interaction-induced Bose metal in two dimensions. Phys. Rev. B 64 (2001) 052507
91. A. Georges, Condensed matter physics with light and atoms: Strongly correlated cold fermions in optical lattices, in: Ultracold Fermi Gases, Varenna School, 2006
92. Góral K., Santos L., and Lewenstein M. Quantum phases of dipolar bosons in optical lattices. Phys. Rev. Lett. 88 (2002) 170406
93. Yi S., Li T., and Sun C.P. Novel quantum phases of dipolar bose gases in optical lattices. Phys. Rev. Lett. 98 (2007) 260405
94. Menotti C., Trefzger C., and Lewenstein M. Metastable states of a gas of dipolar bosons in a 2d optical lattice. Phys. Rev. Lett. 98 (2007) 235301
95. Góral K., Englert B.-G., and Rzażewski K. Semiclassical theory of trapped fermionic dipoles. Phys. Rev. A 63 (2001) 033606
96. Góral K., Brewczyk M., and Rzażewski K. Hydrodynamic excitations of trapped dipolar fermions. Phys. Rev. A 67 (2003) 025601
97. H.T.C. Stoof, M. Houbiers, Condensed matter physics with trapped atomic Fermi gases, in: Bose-Einstein Condensation in Atomic Gases, Varenna School, course CXL, 1999
98. Baranov M.A., Mar'enko M.S., Rychkov Val.S., and Shlyapnikov G.V. Superfluid pairing in a polarized dipolar Fermi gas. Phys. Rev. A 66 (2002) 013606
99. Bardeen J., Cooper L.N., and Schrieffer J.R. Theory of superconductivity. Phys. Rev. 108 (1957) 1175
100. 3He. Rev. Modern Phys. 47 (1975) 331
101. Gor'kov L.P., and Melik-Barkhudarov T.K. Contribution to the theory of superfuidity in an imperfect Fermi gas. Zh. Eksp. Teor. Fiz. 40 (1961) 1452
102. Gor'kov L.P., and Melik-Barkhudarov T.K. Contribution to the theory of superfuidity in an imperfect Fermi gas. Sov. Phys. JETP 13 (1961) 1018
103. Lifshitz E.M., and Pitaevskii L.P. Statistical Phys., Part 2 (1996), Butterworth-Heinemann, Oxford
104. Abrikosov A.A., Gorkov L.P., and Dzialoshinskii I.E. Methods of Quantum Field Theory in Statistical Phys. (1975), Dover, New York
105. Vollhardt D., and Wölfle P. The Superfluid Phases of Helium 3 (1990), Taylor and Francis, London
106. Volovik G.E., and Gor'kov L.P. Superconducting classes in heavy-fermion systems. Zh. Eksp. Teor. Fiz. 88 (1985) 1412
107. Volovik G.E., and Gor'kov L.P. Superconducting classes in heavy-fermion systems. Sov. Phys. JETP 61 (1985) 843
108. Marchenko V.I. On the theory of gauge symmetry of superconductors. Zh. Eksp. Teor. Fiz. 93 (1987) 583
109. Marchenko V.I. On the theory of gauge symmetry of superconductors. Sov. Phys. JETP 66 (1987) 331
110. Sigrist M., and Ueda K. Phenomenological theory of unconventional superconductivity. Rev. Modern Phys. 63 (1991) 239
111. 3: Evidence for unconventional superconductivity. Phys. Rev. Lett. 62 (1989) 1411
112. Baranov M.A., Dobrek Ł., and Lewenstein M. BCS pairing in a trapped dipolar Fermi gas. New J. Phys. 6 (2004) 198
113. Baranov M.A., Dobrek Ł., and Lewenstein M. Superfluidity of trapped dipolar Fermi gases. Phys. Rev. Lett. 92 (2004) 250403
114. Taylor J.R. Scattering Theory (1972), John Wiley & Sons, New York
115. Baranov M.A., and Petrov D.S. Critical temperature and Ginzburg-Landau equation for a trapped Fermi gas. Phys. Rev. A 58 (1998) R801
116. Baranov M.A. Single-particle excitations and the order parameter for a trapped superfluid Fermi gas. Pis'ma Zh. Eksp. Teor. Fiz. 70 (1999) 392
117. Baranov M.A. Single-particle excitations and the order parameter for a trapped superfluid Fermi gas. JETP Lett. 70 (1999) 396
118. Bruun G.M., Castin Y., Dum R., and Burnett K. BCS theory for trapped ultracold fermions. Eur. Phys. J. D 7 (1999) 433
119. Viverit L., Bruun G.M., Minguzzi A., and Fazio R. Pairing fluctuations in trapped fermi gases. Phys. Rev. Lett. 93 (2004) 110406
120. Onsager L. Statistical hydrodynamics. Nuovo Cimento 6 (1949) 249
121. Feynman R.P. Application of quantum mechanics to liquid helium. Prog. Low Temp. Phys. 1 (1955) 17
122. Matthews M.R., Anderson B.P., Haljan P.C., Hall D.S., Wieman C.E., and Cornell E.A. Vortices in a Bose-Einstein condensate. Phys. Rev. Lett. 83 (1999) 2498
123. Madison K.W., Chevy F., Wohlleben W., and Dalibard J. Vortex formation in a stirred Bose-Einstein condensate. Phys. Rev. Lett. 84 (2000) 806
124. Abo-Shaeer J.R., Raman C., Vogels J.M., and Ketterle W. Observation of vortex lattices in Bose-Einstein condensates. Science 292 (2001) 476
125. Raman C., Abo-Shaeer J.R., Vogels J.M., Xu K., and Ketterle W. Vortex nucleation in a stirred Bose-Einstein condensate. Phys. Rev. Lett. 87 (2001) 210402
126. Engels P., Coddington I., Haljan P.C., Schweikhard V., and Cornell E.A. Observation of long-lived vortex aggregates in rapidly rotating Bose-Einstein condensates. Phys. Rev. Lett. 90 (2003) 170405
127. Schweikhard V., Coddington I., Engels P., Mogendorff V.P., and Cornell E.A. Rapidly rotating Bose-Einstein condensates in and near the lowest landau level. Phys. Rev. Lett. 92 (2004) 040404
128. Coddington I., Haljan P.C., Engels P., Schweikhard V., Tung S., and Cornell E.A. Experimental studies of equilibrium vortex properties in a Bose-condensed gas. Phys. Rev. A 70 (2004) 063607
129. Bretin V., Stock S., Seurin Y., and Dalibard J. Fast rotation of a Bose-Einstein condensate. Phys. Rev. Lett. 92 (2004) 050403
130. Wilkin N.K., and Gunn J.M.F. Condensation of "composite Bosons" in a rotating BEC. Phys. Rev. Lett. 84 (2000) 6
131. Cooper N.R., and Wilkin N.K. Composite fermion description of rotating Bose-Einstein condensates. Phys. Rev. B 60 (1999) R16279
132. Viefers S., Hansson T.H., and Reimann S.M. Bose condensates at high angular momenta. Phys. Rev. A 62 (2000) 053604
133. Cooper N.R., Wilkin N.K., and Gunn J.M.F. Quantum phases of vortices in rotating Bose-Einstein condensates. Phys. Rev. Lett. 87 (2001) 120405
134. Lifshitz E.M., and Pitaevskii L.P. Statistical Physica. Part 1 (1980), Pergamon Press Inc., New York
135. Landau L.D., and Lifshitz E.M. The Classical Theory of Fields (1979), Prgamon Press Inc., New York
136. Paredes B., Fedichev P., Cirac J.I., and Zoller P. 1/2-anyons in small atomic Bose-Einstein condensates. Phys. Rev. Lett. 87 (2001) 010402
137. Sinova J., Hanna C.B., and MacDonald A.H. Quantum melting and absence of Bose-Einstein condensation in two-dimensional vortex matter. Phys. Rev. Lett. 89 (2002) 030403
138. Reijnders J.W., van Lankvelt F.J.M., Schoutens K., and Read N. Quantum hall states and Boson triplet condensate for rotating spin-1 Bosons. Phys. Rev. Lett. 89 (2002) 120401
139. Regnault N., and Jolicoeur T. Quantum hall fractions in rotating Bose-Einstein condensates. Phys. Rev. Lett. 91 (2003) 030402
140. Regnault N., and Jolicoeur Th. Quantum hall fractions for spinless bosons. Phys. Rev. B 69 (2004) 235309
141. Regnault N., and Jolicoeur Th. Quantum Hall fractions in ultracold fermionic vapors. Phys. Rev. B 70 (2004) 241307
142. Ho T.L. Bose-Einstein condensates with large number of vortices. Phys. Rev. Lett. 87 (2001) 060403
143. Fischer U.R., and Baym G. Vortex states of rapidly rotating dilute Bose-Einstein condensates. Phys. Rev. Lett. 90 (2003) 140402
144. Baym G., and Pethick C.J. Vortex core structure and global properties of rapidly rotating Bose-Einstein condensates. Phys. Rev. A 69 (2004) 043619
145. Watanabe G., Baym G., and Pethick C.J. Landau levels and the Thomas-Fermi structure of rapidly rotating Bose-Einstein condensates. Phys. Rev. Lett. 93 (2004) 190401
146. Cooper N.R., Komineas S., and Read N. Vortex lattices in the lowest Landau level for confined Bose-Einstein condensates. Phys. Rev. A 70 (2004) 033604
147. Aftalion A., Blanc X., and Dalibard J. Vortex patterns in a fast rotating Bose-Einstein conde. Phys. Rev. A 71 (2005) 023611
148. Wilkin N.K., Gunn J.M.F., and Smith R.A. Do attractive bosons condense?. Phys. Rev. Lett. 80 (1998) 22656
149. Laughlin R.B. Anomalous quantum hall effect: An incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50 (1983) 1395
150. Jain J.K. Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63 (1989) 199
151. Moore G., and Read N. Nonabelions in the fractional quantum hall effect. Nucl. Phys. B360 (1991) 362
152. Read N., and Rezayi E.H. Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level. Phys. Rev. B 59 (1999) 8084
153. O'Dell D.H.J., and Eberlein C. Vortex in a trapped Bose-Einstein condensate with dipole-dipole interactions. Phys. Rev. A 75 (2007) 013604
154. Cooper N.R., Rezayi E.H., and Simon S.H. Vortex lattices in rotating atomic bose gases with dipolar inter. Phys. Rev. Lett. 95 (2005) 200402
155. Haldane F.D.M. Fractional quantization of the hall effect: A hierarchy of incompressible quantum fluid states. Phys. Rev. Lett. 51 (1983) 605
156. Zhang J., and Zhai H. Vortex lattices in planar Bose-Einstein condensates with dipolar interactions. Phys. Rev. Lett. 95 (2005) 200403
157. Yi S., and Pu H. Vortex structures in dipolar condensates. Phys. Rev. A 73 (2006) 061602R
158. Komenias S., and Cooper N.R. Vortex lattices in Bose-Einstein condensates with dipolar interactions beyond the weak-interaction limit. Phys. Rev. A 75 (2007) 023623
159. In: Prange R.E., and Girvin S.M. (Eds). The Quantum Hall Effect (1987), Springer-Verlag, New York
160. Osterloh K., Barberán N., and Lewenstein M. Strongly correlated states of ultracold rotating dipolar Fermi gases. Phys. Rev. Lett. 99 (2007) 100403
161. Baranov M.A., Osterloh K., and Lewenstein M. Fractional quantum hall states in ultracold rapidly rotating dipolar fermi gases. Phys. Rev. Lett. 94 (2005) 070404
162. Fukuyama H. Two dimensional wigner crystallization caused by magnetic field. Solid State Commun. 191 (1976) 55
163. Ziman J.M. Principles of the Theory of Solids (1972), Cambridge University Press, Cambridge
164. Baranov M.A., Fehrmann H., and Lewenstein M. Wigner crystallization in rapidly rotating 2D dipolar Fermi gases. Phys. Rev. Lett. 100 (2008) 200402
165. Maki K., and Zotos X. Static and dynamic properties of a two-dimensional Wigner crystal in a strong magnetic field. Phys. Rev. B 28 (1983) 4349
166. Böttger H. Principles of the Theory of Lattice Dynamics (1983), Physik-Verlag, Weinheim