Q. Condensates, 53 3.2.1 The 2D regime and the quasi-2D regime, p.53

.. Height-of-the-lattice-potential, 67 4.1.3 Axial frequency, atom numbers and dimensionality in the lattice sites, p.71

.. Selecting-sites-from-the-lattice, 72 4.2.1 Adding a magnetic field gradient, p.72

.. Experimental-results, Experimental routine and preliminary experiments, p.78

.. Theoretical-discussion-of-the-results, 107 6.3.1 Introduction of the model, N equal condensates, vol.107

.. Vortex-lattices, 125 7.1.3 Measuring the rotation frequency of a condensate with a vortex lattice, p.127

R. Bosons and H. The, 127 7.2.1 Analogy of rotating neutral particles to electrons in magnetic fields, p.128

.. Landau-levels-for-rotating-particles, 128 7.2.3 Short introduction to the quantum Hall effect in fermionic systems, p.129

L. Bosonic-systems-in-the, 2 The mean field quantum Hall regime, p.131

.. Rotating-bosons-in-anharmonic-traps, 137 8.1.1 The lowest Landau level in an anharmonic trap, p.137

.. Results, 149 9.2.1 Experimental situation, p.150

R. Bibliography, ]. V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Fast rotation of an ultra-cold Bose gas, Phys. Rev. Lett, vol.92, issue.1, p.50403, 2004.

S. Stock, V. Bretin, F. Chevy, and J. Dalibard, Shape oscillation of a rotating Bose-Einstein condensate, Europhysics Letters (EPL), vol.65, issue.5, p.594, 2004.
DOI : 10.1209/epl/i2003-10179-x
URL : https://hal.archives-ouvertes.fr/hal-00000817

Z. Hadzibabic, S. Stock, B. Battelier, V. Bretin, and J. Dalibard, Interference of an Array of Independent Bose-Einstein Condensates, Physical Review Letters, vol.93, issue.18, p.180403, 2004.
DOI : 10.1103/PhysRevLett.93.180403
URL : https://hal.archives-ouvertes.fr/hal-00001592

S. Stock, B. Battelier, V. Bretin, Z. Hadzibabic, and J. Dalibard, Bose-Einstein condensates in fast rotation, Laser Physics Letters, vol.2, issue.6, p.275, 2005.
DOI : 10.1002/lapl.200410177
URL : https://hal.archives-ouvertes.fr/hal-00021948

S. Stock, Z. Hadzibabic, B. Battelier, M. Cheneau, and J. Dalibard, Observation of Phase Defects in Quasi-Two-Dimensional Bose-Einstein Condensates, Physical Review Letters, vol.95, issue.19, p.190403, 2005.
DOI : 10.1103/PhysRevLett.95.190403

Y. Castin, Z. Hadzibabic, S. Stock, J. Dalibard, and S. Stringari, Quantized Vortices in the Ideal Bose Gas: A Physical Realization of Random Polynomials, Physical Review Letters, vol.96, issue.4, p.40405, 2006.
DOI : 10.1103/PhysRevLett.96.040405

D. Guéry-odelin, Dynamique collisionnelle des gaz d'alcalins lourds : du refroidissementévaporatifàmentévaporatifmentévaporatifà la condensation de Bose-Einstein, Laboratoire Kastler Brossel, 1998.

T. Lahaye, Refroidissement parévaporationparévaporation d'un jet atomique guidé magnétiquement, Laboratoire Kastler Brossel, 2005.
DOI : 10.1051/anphys:2006006
URL : https://tel.archives-ouvertes.fr/tel-00011260/document

E. A. Cornell and C. E. Wieman, Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, Reviews of Modern Physics, vol.74, issue.3, p.875, 2002.
DOI : 10.1103/RevModPhys.74.875

W. Ketterle, Nobel lecture: When atoms behave as waves: Bose-Einstein condensation and the atom laser, Reviews of Modern Physics, vol.74, issue.4, p.1131, 2002.
DOI : 10.1103/RevModPhys.74.1131
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.120.1600

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor, Science, vol.269, issue.5221, p.198, 1995.
DOI : 10.1126/science.269.5221.198

K. B. Davis, M. Mewes, M. R. Andrews, N. J. Van-druten, D. S. Durfee et al., Bose-Einstein Condensation in a Gas of Sodium Atoms, Bose-Einstein Condensation in a Gas of Sodium Atoms, pp.3969-3973, 1995.
DOI : 10.1103/PhysRevLett.75.3969

F. Schreck, L. Khaykovich, K. L. Corwin, G. Ferrari, T. Bourdel et al., Quasipure Bose-Einstein Condensate Immersed in a Fermi Sea, Physical Review Letters, vol.87, issue.8, p.80403, 2001.
DOI : 10.1103/PhysRevLett.87.080403
URL : https://hal.archives-ouvertes.fr/hal-00001627

A. Görlitz, J. M. Vogels, A. E. Leanhardt, C. Raman, T. L. Gustavson et al., Realization of Bose-Einstein Condensates in Lower Dimensions, Physical Review Letters, vol.87, issue.13, p.130402, 2001.
DOI : 10.1103/PhysRevLett.87.130402

S. Dettmer, D. Hellweg, P. Ryytty, J. J. Arlt, K. Stengstock et al., Observation of Phase Fluctuations in Elongated Bose-Einstein Condensates, Observation of phase fluctuations in elongated Bose-Einstein condensates, p.160406, 2001.
DOI : 10.1103/PhysRevLett.87.160406

I. Shvarchuck, C. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski et al., Bose-Einstein Condensation into Nonequilibrium States Studied by Condensate Focusing, Bose-Einstein Condensation into Nonequilibrium States Studied by Condensate Focusing, p.270404, 2002.
DOI : 10.1103/PhysRevLett.89.270404
URL : http://arxiv.org/abs/cond-mat/0207599

S. Richard, F. Gerbier, J. H. Thywissen, M. Hugbart, P. Bouyer et al., Momentum Spectroscopy of 1D Phase Fluctuations in Bose-Einstein Condensates, Physical Review Letters, vol.91, issue.1, p.10405, 2003.
DOI : 10.1103/PhysRevLett.91.010405
URL : https://hal.archives-ouvertes.fr/hal-00116296

B. L. Tolra, K. M. O-'hara, J. H. Huckans, W. D. Phillips, S. L. Rolston et al., Observation of Reduced Three-Body Recombination in a Correlated 1D Degenerate Bose Gas, Physical Review Letters, vol.92, issue.19, 2004.
DOI : 10.1103/PhysRevLett.92.190401

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator, Physical Review Letters, vol.92, issue.13, p.130403, 2004.
DOI : 10.1103/PhysRevLett.92.130403

B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling et al., Tonks???Girardeau gas of ultracold atoms in an optical lattice, Nature, vol.42, issue.6989, pp.277-281, 2004.
DOI : 10.1103/PhysRevLett.90.150402
URL : https://hal.archives-ouvertes.fr/hal-00002239

T. Kinoshita, T. Wenger, and D. S. Weiss, Observation of a One-Dimensional Tonks-Girardeau Gas, Science, vol.305, issue.5687, pp.1125-1128, 2004.
DOI : 10.1126/science.1100700

V. Schweikhard, I. Coddington, P. Engels, V. P. Mogendorff, and E. A. Cornell, Rapidly Rotating Bose-Einstein Condensates in and near the Lowest Landau Level, Physical Review Letters, vol.92, issue.4, p.40404, 2004.
DOI : 10.1103/PhysRevLett.92.040404

D. Rychtarik, B. Engeser, H. Nägerl, and R. Grimm, Two-Dimensional Bose-Einstein Condensate in an Optical Surface Trap, Physical Review Letters, vol.92, issue.17, p.173003, 2004.
DOI : 10.1103/PhysRevLett.92.173003

N. L. Smith, W. H. Heathcote, G. Hechenblaikner, E. Nugent, and C. J. Foot, Quasi-2D confinement of a BEC in a combined optical and magnetic potential, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.38, issue.3, pp.223-235, 2005.
DOI : 10.1088/0953-4075/38/3/007

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard et al., Atom Interferometry with Bose-Einstein Condensates in a Double-Well Potential, Physical Review Letters, vol.92, issue.5, p.50405, 2004.
DOI : 10.1103/PhysRevLett.92.050405

M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani et al., Direct Observation of Tunneling and Nonlinear Self-Trapping in a Single Bosonic Josephson Junction, Physical Review Letters, vol.95, issue.1, p.10402, 2005.
DOI : 10.1103/PhysRevLett.95.010402

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth et al., Matter-wave interferometry in a double well on an atom chip, Nature Physics, vol.79, issue.1, p.57, 2005.
DOI : 10.1038/435440a

S. Gupta, K. W. Murch, K. L. Moore, T. P. Purdy, and D. M. Stamper-kurn, Bose-Einstein Condensation in a Circular Waveguide, Einstein Condensation in a Circular Waveguide, p.143201, 2005.
DOI : 10.1103/PhysRevLett.95.143201

I. Bloch, Quantum gases in optical lattices, Physics World, vol.17, issue.4, pp.25-29, 2004.
DOI : 10.1088/2058-7058/17/4/32

O. Morsch and M. Oberthaler, Dynamics of Bose-Einstein condensates in optical lattices, Reviews of Modern Physics, vol.78, issue.1
DOI : 10.1103/RevModPhys.78.179

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, vol.415, p.29, 2002.

M. R. Andrews, C. G. Townsend, H. Miesner, D. S. Durfee, D. M. Kurn et al., Observation of Interference Between Two Bose Condensates, Science, vol.275, issue.5300, pp.637-641, 1997.
DOI : 10.1126/science.275.5300.637

Y. Castin and J. Dalibard, Relative phase of two Bose-Einstein condensates, Physical Review A, vol.55, issue.6, pp.4330-4337, 1997.
DOI : 10.1103/PhysRevA.55.4330

M. Tinkham, Introduction to superconductivity, 1996.

J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, Journal of Physics C: Solid State Physics, vol.6, issue.7, pp.1181-1203, 1973.
DOI : 10.1088/0022-3719/6/7/010

J. M. Kosterlitz, The critical properties of the two-dimensional xy model, Journal of Physics C: Solid State Physics, vol.7, issue.6, p.1046, 1974.
DOI : 10.1088/0022-3719/7/6/005

N. R. Cooper, N. K. Wilkin, and J. M. Gunn, Quantum Phases of Vortices in Rotating Bose-Einstein Condensates, Physical Review Letters, vol.87, issue.12, p.120405, 2001.
DOI : 10.1103/PhysRevLett.87.120405

B. Paredes, P. Fedichev, J. I. Cirac, and P. Zoller, -Anyons in Small Atomic Bose-Einstein Condensates, Physical Review Letters, vol.87, issue.1, p.10402, 2001.
DOI : 10.1103/PhysRevLett.87.010402
URL : https://hal.archives-ouvertes.fr/hal-00908881

D. J. Bishop and J. D. Reppy, Films, Physical Review Letters, vol.40, issue.26, p.1727, 1978.
DOI : 10.1103/PhysRevLett.40.1727

A. I. Safonov, S. A. Vasilyev, I. S. Yasnikov, I. I. Lukashevich, and S. Jaakola, Observation of Quasicondensate in Two-Dimensional Atomic Hydrogen, Physical Review Letters, vol.81, issue.21, p.4545, 1998.
DOI : 10.1103/PhysRevLett.81.4545

R. B. Laughlin, Nobel Lecture: Fractional quantization, Reviews of Modern Physics, vol.71, issue.4, p.863, 1999.
DOI : 10.1103/RevModPhys.71.863

H. L. Stormer, D. C. Tsui, and A. C. Gossard, The fractional quantum Hall effect, Reviews of Modern Physics, vol.71, issue.2, p.298, 1999.
DOI : 10.1103/RevModPhys.71.S298

A. Einstein, Quantentheorie des einatomigen idealen Gases, Sitzungsbericht Preuss, Akad. Wiss., Bericht, vol.22, pp.261-267, 1924.
DOI : 10.1002/3527608958.ch27

F. London, The ??-Phenomenon of Liquid Helium and the Bose-Einstein Degeneracy, Nature, vol.141, issue.3571, p.643, 1938.
DOI : 10.1038/141643a0

S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl et al., Bose-Einstein Condensation of Molecules, Bose-Einstein Condensation of Molecules, p.2101, 2003.
DOI : 10.1126/science.1093280

M. Greiner, C. A. Regal, and D. S. Jin, Emergence of a molecular Bose???Einstein condensate from a Fermi gas, Nature, vol.426, issue.6966, p.537, 2003.
DOI : 10.1038/nature02199

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. Raupach, S. Gupta et al., Observation of Bose-Einstein Condensation of Molecules, Physical Review Letters, vol.91, issue.25, p.250401, 2003.
DOI : 10.1103/PhysRevLett.91.250401

S. Chu, Nobel Lecture: The manipulation of neutral particles, Reviews of Modern Physics, vol.70, issue.3, p.685, 1998.
DOI : 10.1103/RevModPhys.70.685

C. N. Cohen-tannoudji, Nobel Lecture: Manipulating atoms with photons, Reviews of Modern Physics, vol.70, issue.3, p.707, 1998.
DOI : 10.1103/RevModPhys.70.707

W. D. Phillips, Nobel Lecture: Laser cooling and trapping of neutral atoms, Reviews of Modern Physics, vol.70, issue.3, p.721, 1998.
DOI : 10.1103/RevModPhys.70.721

H. F. Hess, Evaporative cooling of magnetically trapped and compressed spin-polarized hydrogen, Physical Review B, vol.34, issue.5, p.3476, 1986.
DOI : 10.1103/PhysRevB.34.3476

K. B. Davis, M. Mewes, M. A. Joffe, M. R. Andrews, and W. Ketterle, Evaporative Cooling of Sodium Atoms, Physical Review Letters, vol.74, issue.26, pp.5202-5205, 1995.
DOI : 10.1103/PhysRevLett.74.5202

K. B. Davis, M. Mewes, and W. Ketterle, An analytical model for evaporative cooling of atoms, Applied Physics B Laser and Optics, vol.45, issue.196, pp.155-159, 1995.
DOI : 10.1007/BF01135857

O. J. Luiten, M. W. Reynolds, and J. T. Walraven, Kinetic theory of the evaporative cooling of a trapped gas, Physical Review A, vol.53, issue.1, p.381, 1996.
DOI : 10.1103/PhysRevA.53.381

C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, 2002.
DOI : 10.1017/cbo9780511755583
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.382.7192

V. Bagnato, D. E. Pritchard, and D. Kleppner, Bose-Einstein condensation in an external potential, Physical Review A, vol.35, issue.10, p.4354, 1987.
DOI : 10.1103/PhysRevA.35.4354

N. N. Bogoliubov, ON THE THEORY OF SUPERFLUIDITY, J. Phys. (USSR), vol.11, issue.23, 1947.
DOI : 10.1016/B978-0-08-015816-7.50020-1

]. W. Ketterle, D. S. Durfee, and D. M. Stamper-kurn, Making, probing and understanding Bose-Einstein condensates, Bose-Einstein condensation in atomic gases, Proceedings of the International School of Physics Enrico Fermi, Course CXL, pp.67-176, 1999.

S. Stringari, Collective Excitations of a Trapped Bose-Condensed Gas, Physical Review Letters, vol.77, issue.12, pp.2360-2363, 1996.
DOI : 10.1103/PhysRevLett.77.2360

P. Ohberg, E. L. Surkov, I. Tittonen, S. Stenholm, M. Wilkens et al., Low-energy elementary excitations of a trapped Bose-condensed gas, Physical Review A, vol.56, issue.5, p.3346, 1997.
DOI : 10.1103/PhysRevA.56.R3346

S. Stringari, Dynamics of Bose-Einstein condensed gases in highly deformed traps, Physical Review A, vol.58, issue.3, p.2385, 1998.
DOI : 10.1103/PhysRevA.58.2385

D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Collective Excitations of a Bose-Einstein Condensate in a Dilute Gas, Physical Review Letters, vol.77, issue.3, p.420, 1996.
DOI : 10.1103/PhysRevLett.77.420

F. Chevy, V. Bretin, P. Rosenbusch, K. Madison, and J. Dalibard, Transverse Breathing Mode of an Elongated Bose-Einstein Condensate, Physical Review Letters, vol.88, issue.25, p.250402, 2002.
DOI : 10.1103/PhysRevLett.88.250402
URL : https://hal.archives-ouvertes.fr/hal-00002531

L. P. Pitaevskii and A. Rosch, Breathing modes and hidden symmetry of trapped atoms in two dimensions, Physical Review A, vol.55, issue.2, p.853, 1997.
DOI : 10.1103/PhysRevA.55.R853

C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, and M. A. Kasevich, Squeezed States in a Bose-Einstein Condensate, Squeezed states in a Bose-Einstein condensate, p.2386, 2001.
DOI : 10.1126/science.1058149

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Görlitz et al., Observation of phase-coherent amplification of atomic matter waves, Nature, vol.402, issue.6762, pp.641-644, 1999.
DOI : 10.1038/45194

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga et al., Phase-Coherent Amplification of Matter Waves, Phase coherent amplification of matter waves, pp.2309-2312, 1999.
DOI : 10.1126/science.286.5448.2309

I. Bloch, T. W. Hänsch, and T. Esslinger, Atom Laser with a cw Output Coupler, Physical Review Letters, vol.82, issue.15, p.3008, 1999.
DOI : 10.1103/PhysRevLett.82.3008

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson et al., A Well-Collimated Quasi-Continuous Atom Laser, Well-Collimated Quasi-Continuous Atom Laser, pp.1706-1709, 1999.
DOI : 10.1126/science.283.5408.1706

T. Lahaye, J. M. Vogels, K. Guenter, Z. Wang, J. Dalibard et al., Realization of a Magnetically Guided Atomic Beam in the Collisional Regime, Physical Review Letters, vol.93, issue.9, p.93003, 2004.
DOI : 10.1103/PhysRevLett.93.093003
URL : https://hal.archives-ouvertes.fr/hal-00001508

D. S. Petrov, M. Holzmann, and G. V. Shlyapnikov, Bose-Einstein Condensation in Quasi-2D Trapped Gases, Bose-Einstein Condensation in Quasi- 2D Trapped Gases, p.2551, 2000.
DOI : 10.1103/PhysRevLett.84.2551
URL : https://hal.archives-ouvertes.fr/hal-00001658

D. S. Petrov, D. M. Gangardt, and G. V. Shlyapnikov, Low-dimensional trapped gases, Journal de Physique IV (Proceedings), vol.116, pp.5-44, 2004.
DOI : 10.1051/jp4:2004116001
URL : https://hal.archives-ouvertes.fr/hal-00003349

R. H. Brown and R. Q. Twiss, Correlation between Photons in two Coherent Beams of Light, Nature, vol.45, issue.4497, p.27, 1956.
DOI : 10.1038/177027a0

R. H. Brown and R. Q. Twiss, LXXIV. A new type of interferometer for use in radio astronomy, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol.3, issue.366, p.663, 1954.
DOI : 10.1002/andp.19153532104

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke et al., Spatial quantum noise interferometry in expanding ultracold atom clouds, Nature, vol.22, issue.7032, p.481, 2005.
DOI : 10.1103/PhysRevA.59.4595

P. Kapitza, Viscosity of Liquid Helium below the ??-Point, Nature, vol.141, issue.3558, p.74, 1938.
DOI : 10.1038/141074a0

J. F. Allen and A. D. Misener, Flow of Liquid Helium II, Nature, vol.141, issue.3558, p.75, 1938.
DOI : 10.1038/141075a0

F. London, On the Bose-Einstein Condensation, Physical Review, vol.54, issue.11, p.947, 1938.
DOI : 10.1103/PhysRev.54.947

A. J. Leggett, Superfluidity, Reviews of Modern Physics, vol.71, issue.2, p.318, 1999.
DOI : 10.1103/RevModPhys.71.S318

D. Guéry-odelin, J. Söding, P. Desbiolles, and J. Dalibard, Is Bose-Einstein condensation of atomic cesium possible?, Europhysics Letters (EPL), vol.44, issue.1, p.25, 1998.
DOI : 10.1209/epl/i1998-00425-9

T. Weber, J. Herbig, M. Mark, H. Nägerl, and R. Grimm, Bose-Einstein Condensation of Cesium, Science, vol.299, issue.5604, pp.232-235, 2003.
DOI : 10.1126/science.1079699

J. Dalibard and C. Cohen-tannoudji, Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, Journal of the Optical Society of America B, vol.6, issue.11, p.2023, 1989.
DOI : 10.1364/JOSAB.6.002023

C. Cohen-tannoudji, Piégeage non dissipatif et refroidissementévaporatifrefroidissementévaporatif Cours duColì ege de France, available online on http, 1996.

W. Paul, Electromagnetic traps for charged and neutral particles, Reviews of Modern Physics, vol.62, issue.3, p.531, 1990.
DOI : 10.1103/RevModPhys.62.531
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.487.6288

Y. Castin and R. Dum, Bose-Einstein Condensates in Time Dependent Traps, Physical Review Letters, vol.77, issue.27, pp.5315-5319, 1996.
DOI : 10.1103/PhysRevLett.77.5315

Y. Kagan, E. L. Surkov, and G. V. Shlyapnikov, Evolution of a Bose-condensed gas under variations of the confining potential, Physical Review A, vol.54, issue.3, pp.1753-1756, 1996.
DOI : 10.1103/PhysRevA.54.R1753

D. Hellweg, L. Cacciapuoti, M. Kottke, T. Schulte, K. Sengstock et al., Measurement of the Spatial Correlation Function of Phase Fluctuating Bose-Einstein Condensates, Physical Review Letters, vol.91, issue.1, p.10406, 2003.
DOI : 10.1103/PhysRevLett.91.010406

Y. Colombe, E. Knyazchyan, O. Morizot, B. Mercier, V. Lorent et al., Ultracold atoms confined in rf-induced two-dimensional trapping potentials, Europhysics Letters (EPL), vol.67, issue.4, p.593, 2004.
DOI : 10.1209/epl/i2004-10095-7
URL : https://hal.archives-ouvertes.fr/hal-00001226

N. D. Mermin and H. Wagner, Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models, Physical Review Letters, vol.17, issue.22, p.1133, 1966.
DOI : 10.1103/PhysRevLett.17.1133

P. C. Hohenberg, Existence of Long-Range Order in One and Two Dimensions, Physical Review, vol.158, issue.2, p.383, 1967.
DOI : 10.1103/PhysRev.158.383

N. D. Mermin, Crystalline Order in Two Dimensions, Physical Review, vol.176, issue.1, p.250, 1968.
DOI : 10.1103/PhysRev.176.250

W. Kane and L. Kadanoff, Long-Range Order in Superfluid Helium, Physical Review, vol.155, issue.1, p.80, 1967.
DOI : 10.1103/PhysRev.155.80

V. Berezinskii, Destruction of long-range order in one-dimensional and 2-dimensional systems having a continuous symmetry group, 1 -classical systems, Sov. Phys. JETP- USSR, vol.32, p.493, 1971.

V. Berezinskii, Destruction of long-range order in one-dimensional and 2-dimensional systems having a continuous symmetry group, 2 -quantum systems, Sov. Phys. JETP- USSR, vol.34, p.610, 1972.

V. Bagnato and D. Kleppner, Bose-Einstein condensation in low-dimensional traps, Physical Review A, vol.44, issue.11, p.7439, 1991.
DOI : 10.1103/PhysRevA.44.7439

J. O. Andersen, U. A. Khawaja, and H. T. Stoof, Phase Fluctuations in Atomic Bose Gases, Phase Fluctuations in Atomic Bose Gases, p.70407, 2002.
DOI : 10.1103/PhysRevLett.88.070407

T. Ho and M. Ma, Quasi 1 and 2d Dilute Bose Gas in Magnetic Traps: Existence of Off-Diagonal Order and Anomalous Quantum Fluctuations, Journal of Low Temperature Physics, vol.115, issue.1/2, p.61, 1999.
DOI : 10.1023/A:1021894713105

M. Kardar, MIT lecture notes: Statistical mechanics of fields, 2004.

Y. Castin and R. Dum, Bose-Einstein condensates with vortices in rotating traps, The European Physical Journal D, vol.7, issue.3, pp.399-412, 1999.
DOI : 10.1007/s100530050584

V. N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics, 1983.

N. Prokof-'ev, O. Ruebenacker, and B. Svistunov, Critical Point of a Weakly Interacting Two-Dimensional Bose Gas, Physical Review Letters, vol.87, issue.27, p.270402, 2001.
DOI : 10.1103/PhysRevLett.87.270402

D. R. Nelson and J. M. Kosterlitz, Universal Jump in the Superfluid Density of Two-Dimensional Superfluids, Physical Review Letters, vol.39, issue.19, p.1201, 1977.
DOI : 10.1103/PhysRevLett.39.1201

D. J. Thouless, Topological Quantum Numbers in Nonrelativistic Physics, 1998.

T. P. Simula, M. D. Lee, and D. A. Hutchinson, Transition from the Bose???Einstein condensate to the Berezinskii???Kosterlitz???Thouless phase, to appear in Philosophical Magazine Letters, p.412512, 2004.
DOI : 10.1103/PhysRevA.66.035601

T. P. Simula and P. B. Blakie, Thermal activation of vortex-antivortex pairs in quasi-2D Bose-Einstein condensates, p.510097, 2005.

M. Holzmann, G. Baym, J. Blaizot, and F. Laloë, The Kosterlitz-Thouless-Berezinskii transition of homogeneous and trapped Bose gases in two dimensions, p.508131, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00007809

S. Burger, F. S. Cataliotti, C. Fort, P. Maddaloni, F. Minardi et al., Einstein condensation in an optical lattice, Europhys. Lett, vol.57, issue.1, 2002.

M. Köhl, H. Moritz, T. Stöferle, C. Schori, and T. Esslinger, Superfluid to Mott insulator transition in one, two, and three dimensions, Journal of Low Temperature Physics, vol.86, issue.3-4, p.635, 2005.
DOI : 10.1007/s10909-005-2273-4

H. Ott, E. De-mirandes, F. Ferlaino, G. Roati, V. Türck et al., Radio Frequency Selective Addressing of Localized Atoms in a Periodic Potential, Physical Review Letters, vol.93, issue.12, p.120407, 2004.
DOI : 10.1103/PhysRevLett.93.120407

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel et al., Neutral Atom Quantum Register, Physical Review Letters, vol.93, issue.15, p.150501, 2004.
DOI : 10.1103/PhysRevLett.93.150501

R. Grimm, M. Weidenmüller, and Y. B. Ovchinnikov, Optical Dipole Traps for Neutral Atoms, p.9902072, 1999.
DOI : 10.1016/S1049-250X(08)60186-X

S. Altshuler, L. M. Frantz, and R. Braunstein, Reflection of Atoms from Standing Light Waves, Physical Review Letters, vol.17, issue.5, p.231, 1966.
DOI : 10.1103/PhysRevLett.17.231

P. L. Gould, G. A. Ruff, and D. E. Pritchard, Diffraction of atoms by light, American Journal of Physics, vol.62, issue.11, p.827, 1986.
DOI : 10.1119/1.17706

J. Denschlag, J. Simsarian, H. Häffner, C. Mckenzie, A. Browaeys et al., A Bose-Einstein condensate in an optical lattice, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.35, issue.14, p.3095, 2002.
DOI : 10.1088/0953-4075/35/14/307

Y. Castin, Les limites du refroidissement laser dans les mélasses optiquesàoptiquesà une dimension, 1992.

G. Hechenblaikner, J. M. Krueger, and C. J. Foot, Properties of quasi-two-dimensional condensates in highly anisotropic traps, Physical Review A, vol.71, issue.1, p.13604, 2005.
DOI : 10.1103/PhysRevA.71.013604

K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Vortex Formation in a Stirred Bose-Einstein Condensate, Physical Review Letters, vol.84, issue.5, pp.806-809, 2000.
DOI : 10.1103/PhysRevLett.84.806

F. Chevy, K. Madison, V. Bretin, and J. Dalibard, Interferometric detection of a single vortex in a dilute Bose-Einstein condensate, Physical Review A, vol.64, issue.3, p.31601, 2001.
DOI : 10.1103/PhysRevA.64.031601
URL : https://hal.archives-ouvertes.fr/hal-00002530

E. L. Bolda and D. F. Walls, Detection of Vorticity in Bose-Einstein Condensed Gases by Matter-Wave Interference, Physical Review Letters, vol.81, issue.25, p.5477, 1998.
DOI : 10.1103/PhysRevLett.81.5477

J. Tempere and J. T. Devreese, Fringe pattern of interfering bose???einstein condensates with a vortex, Solid State Communications, vol.108, issue.12, p.993, 1998.
DOI : 10.1016/S0038-1098(98)90448-3

S. Inouye, S. Gupta, T. Rosenband, A. P. Chikkatur, A. Görlitz et al., Observation of Vortex Phase Singularities in Bose-Einstein Condensates, Observation of vortex phase singularities in Bose-Einstein condensates, p.80402, 2001.
DOI : 10.1103/PhysRevLett.87.080402

S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock et al., Dark Solitons in Bose-Einstein Condensates, Physical Review Letters, vol.83, issue.25, p.5198, 1999.
DOI : 10.1103/PhysRevLett.83.5198

D. L. Feder, M. S. Pindzola, L. A. Collins, B. I. Schneider, and C. W. Clark, Dark-soliton states of Bose-Einstein condensates in anisotropic traps, Physical Review A, vol.62, issue.5, p.53606, 2000.
DOI : 10.1103/PhysRevA.62.053606

F. Dalfovo and M. Modugno, Free expansion of Bose-Einstein condensates with quantized vortices, Physical Review A, vol.61, issue.2, p.23605, 2000.
DOI : 10.1103/PhysRevA.61.023605

K. Sheshadri, H. R. Krishnamurthy, R. Pandit, and T. V. Ramakrishnan, Superfluid and Insulating Phases in an Interacting-Boson Model: Mean-Field Theory and the RPA, Europhysics Letters (EPL), vol.22, issue.4, p.257, 1993.
DOI : 10.1209/0295-5075/22/4/004

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Cold Bosonic Atoms in Optical Lattices, Physical Review Letters, vol.81, issue.15, p.3108, 1998.
DOI : 10.1103/PhysRevLett.81.3108

J. Hecker-denschlag, J. E. Simsarian, H. Häffner, C. Mckenzie, A. Browaeys et al., A Bose-Einstein condensate in an optical lattice, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.35, issue.14, pp.3095-3110, 2002.
DOI : 10.1088/0953-4075/35/14/307

P. Pedri, L. Pitaevskii, S. Stringari, C. Fort, S. Burger et al., Expansion of a Coherent Array of Bose-Einstein Condensates, Physical Review Letters, vol.87, issue.22, p.220401, 2001.
DOI : 10.1103/PhysRevLett.87.220401

J. Javanainen and S. M. Yoo, Quantum Phase of a Bose-Einstein Condensate with an Arbitrary Number of Atoms, Physical Review Letters, vol.76, issue.2, pp.161-164, 1996.
DOI : 10.1103/PhysRevLett.76.161

M. Naraschewski, H. Wallis, A. Schenzle, J. I. Cirac, and P. Zoller, Interference of Bose condensates, Physical Review A, vol.54, issue.3, pp.2185-2196, 1996.
DOI : 10.1103/PhysRevA.54.2185

M. Lewenstein and L. You, Quantum Phase Diffusion of a Bose-Einstein Condensate, Physical Review Letters, vol.77, issue.17, pp.3489-3493, 1996.
DOI : 10.1103/PhysRevLett.77.3489

J. Javanainen and M. Wilkens, Phase and Phase Diffusion of a Split Bose-Einstein Condensate, Physical Review Letters, vol.78, issue.25, pp.4675-4678, 1997.
DOI : 10.1103/PhysRevLett.78.4675

A. J. Leggett and F. Sols, Comment on ???Phase and Phase Diffusion of a Split Bose-Einstein Condensate???, Physical Review Letters, vol.81, issue.6, p.1344, 1998.
DOI : 10.1103/PhysRevLett.81.1344

J. Javanainen and M. Wilkens, Javanainen and Wilkens Reply:, Physical Review Letters, vol.81, issue.6, p.1345, 1998.
DOI : 10.1103/PhysRevLett.81.1345

J. A. Dunningham, M. J. Collett, and D. F. Walls, Quantum state of a trapped Bose-Einstein condensate, Physics Letters A, vol.245, issue.1-2, p.49, 1998.
DOI : 10.1016/S0375-9601(98)00386-7

C. Menotti, J. R. Anglin, J. I. Cirac, and P. Zoller, Dynamic splitting of a Bose-Einstein condensate, Physical Review A, vol.63, issue.2, p.23601, 2001.
DOI : 10.1103/PhysRevA.63.023601

P. W. Anderson, The Lesson of Quantum Theory, pp.23-34, 1986.

E. Altman, E. Demler, and M. D. Lukin, Probing many-body states of ultracold atoms via noise correlations, Physical Review A, vol.70, issue.1, p.13603, 2004.
DOI : 10.1103/PhysRevA.70.013603

R. Bach and K. Rzazewski, Correlation functions of cold bosons in an optical lattice, Physical Review A, vol.70, issue.6, p.63622, 2004.
DOI : 10.1103/PhysRevA.70.063622

C. M. Caves, Quantum-mechanical noise in an interferometer, Physical Review D, vol.23, issue.8, p.1693, 1981.
DOI : 10.1103/PhysRevD.23.1693

W. Zwerger, Mott??Hubbard transition of cold atoms in optical lattices, Journal of Optics B: Quantum and Semiclassical Optics, vol.5, issue.2, pp.9-16, 2003.
DOI : 10.1088/1464-4266/5/2/352

M. Greiner, C. A. Regal, J. T. Stewart, and D. S. Jin, Probing Pair-Correlated Fermionic Atoms through Correlations in Atom Shot Noise, Physical Review Letters, vol.94, issue.11, p.110401, 2005.
DOI : 10.1103/PhysRevLett.94.110401

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman et al., Vortices in a Bose-Einstein Condensate, Vortices in a Bose-Einstein Condensate, p.2498, 1999.
DOI : 10.1103/PhysRevLett.83.2498

J. R. Abo-shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of Vortex Lattices in Bose-Einstein Condensates, Observation of Vortex Lattices in Bose-Einstein Condensates, pp.476-479, 2001.
DOI : 10.1126/science.1060182

E. Hodby, G. Hechenblaikner, S. A. Hopkins, O. M. Maragò, and C. J. Foot, Vortex Nucleation in Bose-Einstein Condensates in an Oblate, Purely Magnetic Potential, Physical Review Letters, vol.88, issue.1, p.10405, 2002.
DOI : 10.1103/PhysRevLett.88.010405

P. C. Haljan, I. Coddington, P. Engels, and E. A. Cornell, Driving Bose-Einstein-Condensate Vorticity with a Rotating Normal Cloud, Physical Review Letters, vol.87, issue.21, p.210403, 2001.
DOI : 10.1103/PhysRevLett.87.210403

P. Engels, I. Coddington, P. C. Haljan, V. Schweikhard, and E. A. Cornell, Observation of Long-Lived Vortex Aggregates in Rapidly Rotating Bose-Einstein Condensates, Physical Review Letters, vol.90, issue.17, p.170405, 2003.
DOI : 10.1103/PhysRevLett.90.170405

S. Stringari, Phase Diagram of Quantized Vortices in a Trapped Bose-Einstein Condensed Gas, Physical Review Letters, vol.82, issue.22, p.4371, 1999.
DOI : 10.1103/PhysRevLett.82.4371

M. A. Cazalilla, Surface modes of ultra-cold atomic clouds with very large number of vortices, Phys. Rev. A, vol.67, p.33613, 2003.

K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, Stationary States of a Rotating Bose-Einstein Condensate: Routes to Vortex Nucleation, Physical Review Letters, vol.86, issue.20, p.4443, 2001.
DOI : 10.1103/PhysRevLett.86.4443
URL : https://hal.archives-ouvertes.fr/hal-00002550

C. Raman, J. R. Abo-shaeer, J. M. Vogels, K. Xu, and W. Ketterle, Vortex Nucleation in a Stirred Bose-Einstein Condensate, Physical Review Letters, vol.87, issue.21, p.210402, 2001.
DOI : 10.1103/PhysRevLett.87.210402

T. Ho, Bose-Einstein Condensates with Large Number of Vortices, Physical Review Letters, vol.87, issue.6, p.60403, 2001.
DOI : 10.1103/PhysRevLett.87.060403

N. Regnault and T. Jolicoeur, Quantum Hall Fractions in Rotating Bose-Einstein Condensates, Physical Review Letters, vol.91, issue.3, p.30402, 2003.
DOI : 10.1103/PhysRevLett.91.030402
URL : https://hal.archives-ouvertes.fr/hal-00122417

U. R. Fischer, P. O. Fedichev, and A. Recati, Vortex liquids and vortex quantum Hall states in trapped rotating Bose gases, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.37, issue.7, p.301, 2002.
DOI : 10.1088/0953-4075/37/7/074

R. P. Feynman, Progress in Low Temperature Physics, 1955.

V. K. Tkachenko, On Vortex Lattices, Sov. Phys, Zh. Eksp. Teor. Fiz 49, pp.1282-1875, 1965.

F. Chevy, K. Madison, and J. Dalibard, Measurement of the Angular Momentum of a Rotating Bose-Einstein Condensate, Physical Review Letters, vol.85, issue.11, p.2223, 2000.
DOI : 10.1103/PhysRevLett.85.2223
URL : https://hal.archives-ouvertes.fr/hal-00002549

N. R. Cooper and N. K. Wilkin, Composite fermion description of rotating Bose-Einstein condensates, Physical Review B, vol.60, issue.24, p.16279, 1999.
DOI : 10.1103/PhysRevB.60.R16279

B. Mottelson, Yrast Spectra of Weakly Interacting Bose-Einstein Condensates, Physical Review Letters, vol.83, issue.14, p.2695, 1999.
DOI : 10.1103/PhysRevLett.83.2695

N. K. Wilkin and J. M. Gunn, Condensation of ???Composite Bosons??? in a Rotating BEC, Physical Review Letters, vol.84, issue.1, p.6, 2000.
DOI : 10.1103/PhysRevLett.84.6

K. Klitzing, The quantized Hall effect, Reviews of Modern Physics, vol.58, issue.3, p.519, 1986.
DOI : 10.1103/RevModPhys.58.519

D. R. Yennie, Integral quantum Hall effect for nonspecialists, Reviews of Modern Physics, vol.59, issue.3, p.781, 1987.
DOI : 10.1103/RevModPhys.59.781

Z. Chen, B. Zhao, and Y. Zhang, Quantum Hall effect in a rotating Bose-Einstein condensate : an atomic twin of the electronic brother, p.211187, 2002.

J. Sinova, C. B. Hanna, and A. H. Macdonald, Quantum Melting and Absence of Bose-Einstein Condensation in Two-Dimensional Vortex Matter, Physical Review Letters, vol.89, issue.3, p.30403, 2002.
DOI : 10.1103/PhysRevLett.89.030403

B. Paredes, P. Zoller, and J. I. Cirac, Fermionizing a small gas of ultracold bosons, Physical Review A, vol.66, issue.3, p.33609, 2002.
DOI : 10.1103/PhysRevA.66.033609

J. Sinova, C. B. Hanna, and A. H. Macdonald, Measuring the Condensate Fraction of Rapidly Rotating Trapped Boson Systems: Off-Diagonal Order from the Density Profile, Physical Review Letters, vol.90, issue.12, p.120401, 2003.
DOI : 10.1103/PhysRevLett.90.120401

N. Regnault and T. Jolicoeur, Quantum Hall fractions for spinless bosons, Physical Review B, vol.69, issue.23, p.235309, 2004.
DOI : 10.1103/PhysRevB.69.235309
URL : https://hal.archives-ouvertes.fr/hal-00000939

T. Nakajima and M. Ueda, Energy gaps and roton structure above the ? = 1
DOI : 10.1103/physrevlett.91.140401

N. Read and N. R. Cooper, Free expansion of lowest-Landau-level states of trapped atoms: A wave-function microscope, Physical Review A, vol.68, issue.3, p.35601, 2003.
DOI : 10.1103/PhysRevA.68.035601

U. R. Fischer and G. Baym, Vortex States of Rapidly Rotating Dilute Bose-Einstein Condensates, Physical Review Letters, vol.90, issue.14, p.140402, 2003.
DOI : 10.1103/PhysRevLett.90.140402

I. Coddington, P. C. Haljan, P. Engels, V. Schweikhard, S. Tung et al., Experimental studies of equilibrium vortex properties in a Bose-condensed gas, Physical Review A, vol.70, issue.6, p.63607, 2004.
DOI : 10.1103/PhysRevA.70.063607

E. Bogomolny, O. Bohigas, and P. Leboeuf, Distribution of roots of random polynomials, Physical Review Letters, vol.68, issue.18, p.2726, 1992.
DOI : 10.1103/PhysRevLett.68.2726
URL : https://hal.archives-ouvertes.fr/in2p3-00004754

J. H. Hannay, Chaotic analytic zero points: exact statistics for those of a random spin state, Journal of Physics A: Mathematical and General, vol.29, issue.5, p.101, 1996.
DOI : 10.1088/0305-4470/29/5/004

P. Leboeuf, Random analytic chaotic eigenstates, Journal of Statistical Physics, vol.95, issue.3/4, p.651, 1999.
DOI : 10.1023/A:1004595310043
URL : https://hal.archives-ouvertes.fr/hal-00003969

N. R. Cooper, F. J. Van-lankvelt, J. W. Reijnders, and K. Schoutens, Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries, Physical Review A, vol.72, issue.6, p.508031, 2005.
DOI : 10.1103/PhysRevA.72.063622

P. Rosenbusch, D. Petrov, S. Sinha, F. Chevy, V. Bretin et al., Critical Rotation of a Harmonically Trapped Bose Gas, Physical Review Letters, vol.88, issue.25, p.250403, 2002.
DOI : 10.1103/PhysRevLett.88.250403
URL : https://hal.archives-ouvertes.fr/hal-00002249

A. L. Fetter, Rotating vortex lattice in a Bose-Einstein condensate trapped in combined quadratic and quartic radial potentials, Physical Review A, vol.64, issue.6, p.63608, 2001.
DOI : 10.1103/PhysRevA.64.063608

E. Lundh, Multiply quantized vortices in trapped Bose-Einstein condensates, Physical Review A, vol.65, issue.4, p.43604, 2002.
DOI : 10.1103/PhysRevA.65.043604

K. Kasamatsu, M. Tsubota, and M. Ueda, Giant hole and circular superflow in a fast rotating Bose-Einstein condensate, Physical Review A, vol.66, issue.5, p.53606, 2002.
DOI : 10.1103/PhysRevA.66.053606

G. M. Kavoulakis and G. Baym, Rapidly rotating Bose-Einstein condensates in anharmonic traps, New Journal of Physics, vol.5, issue.51, pp.1-51, 2003.

A. Aftalion and I. Danaila, Three-dimensional vortex configurations in a rotating Bose-Einstein condensate, Physical Review A, vol.68, issue.2, p.23603, 2003.
DOI : 10.1103/PhysRevA.68.023603
URL : https://hal.archives-ouvertes.fr/hal-00008637

A. D. Jackson, G. M. Kavoulakis, and E. Lundh, Phase diagram of a rotating Bose-Einstein condensate with anharmonic confinement, Physical Review A, vol.69, issue.5, p.53619, 2004.
DOI : 10.1103/PhysRevA.69.053619

F. Zambelli and S. Stringari, Quantized Vortices and Collective Oscillations of a Trapped Bose-Einstein Condensate, Physical Review Letters, vol.81, issue.9, p.1754, 1998.
DOI : 10.1103/PhysRevLett.81.1754

P. Rosenbusch, V. Bretin, and J. Dalibard, Dynamics of a Single Vortex Line in a Bose-Einstein Condensate, Physical Review Letters, vol.89, issue.20, p.200403, 2002.
DOI : 10.1103/PhysRevLett.89.200403
URL : https://hal.archives-ouvertes.fr/hal-00002528

E. Lundh, C. J. Pethick, and H. Smith, Vortices in Bose-Einstein-condensed atomic clouds, Physical Review A, vol.58, issue.6, p.4816, 1998.
DOI : 10.1103/PhysRevA.58.4816

P. Engels, I. Coddington, P. C. Haljan, and E. A. Cornell, Nonequilibrium Effects of Anisotropic Compression Applied to Vortex Lattices in Bose-Einstein Condensates, Physical Review Letters, vol.89, issue.10, p.100403, 2002.
DOI : 10.1103/PhysRevLett.89.100403

W. Ketterle and N. J. Van-druten, Evaporative Cooling of Trapped Atoms, Advances in Atomic, Molecular, and Optical Physics, vol.37, pp.181-236, 1996.
DOI : 10.1016/S1049-250X(08)60101-9

E. Akkermans and S. Ghosh, Composite bosons description of rapidly rotating Bose- Einstein condensates, p.307418, 2003.

I. Danaila, Three-dimensional vortex structure of a fast rotating Bose-Einstein condensate with harmonic-plus-quartic confinement, Physical Review A, vol.72, issue.1, p.13605, 2005.
DOI : 10.1103/PhysRevA.72.013605

G. Baym and C. J. Pethick, Vortex core structure and global properties of rapidly rotating Bose-Einstein condensates, Physical Review A, vol.69, issue.4, p.43619, 2004.
DOI : 10.1103/PhysRevA.69.043619

I. Coddington, P. C. Haljan, V. Schweikhard, and E. A. Cornell, Observation of Tkachenko Oscillations in Rapidly Rotating Bose-Einstein Condensates, Physical Review Letters, vol.91, issue.10, p.100402, 2003.
DOI : 10.1103/PhysRevLett.91.100402

M. Tsubota, K. Kasamatsu, and A. Tsunehiko, Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates, Journal of Low Temperature Physics, vol.90, issue.3-4, p.631, 2003.
DOI : 10.1007/s10909-005-2236-9

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Reviews of Modern Physics, vol.71, issue.3, p.463, 1999.
DOI : 10.1103/RevModPhys.71.463

M. Cozzini and S. Stringari, Macroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice, Physical Review A, vol.67, issue.4, p.41602, 2003.
DOI : 10.1103/PhysRevA.67.041602

A. Sedrakian and I. Wasserman, Oscillations of rotating trapped Bose-Einstein condensates, Physical Review A, vol.63, issue.6, p.63605, 2001.
DOI : 10.1103/PhysRevA.63.063605

F. Chevy and S. Stringari, Kelvin modes of a fast rotating Bose-Einstein condensate, Physical Review A, vol.68, issue.5, p.53601, 2003.
DOI : 10.1103/PhysRevA.68.053601
URL : https://hal.archives-ouvertes.fr/hal-00148467

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Course of Theoretical Physics, 1981.

M. Tsubota, K. Kasamatsu, and A. Tsunehiko, Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates, Journal of Low Temperature Physics, vol.90, issue.3-4, p.631, 2003.
DOI : 10.1007/s10909-005-2236-9

J. Martikainen and H. T. Stoof, Quantum Fluctuations of a Vortex in an Optical Lattice, Physical Review Letters, vol.91, issue.24, p.240403, 2003.
DOI : 10.1103/PhysRevLett.91.240403

J. Martikainen and H. T. Stoof, Vortex-Line Solitons in A Periodically Modulated Bose-Einstein Condensate, Physical Review Letters, vol.93, issue.7, p.70402, 2004.
DOI : 10.1103/PhysRevLett.93.070402

J. Martikainen and H. T. Stoof, Quantum theory of a vortex line in an optical lattice, Physical Review A, vol.69, issue.5, p.53617, 2004.
DOI : 10.1103/PhysRevA.69.053617

J. Martikainen and H. T. Stoof, Spontaneous squeezing of a vortex in an optical lattice, Physical Review A, vol.70, issue.1, p.13604, 2004.
DOI : 10.1103/PhysRevA.70.013604