.. Le-phénomène-de-condensation-de-bose-eintein, 28 1.2.1 Une inversion d'ellipticité, 28 1.2.2 Interprétation : saturation desétatsdesétats excités . . . . . . . . . . . . . . . . . 29

.. Dynamique-d-'un-condensat, 34 1.4.1 Description hydrodynamique, p.36

). Ou-presque, 44 2.3.1 Lois d'´ echelle pour le monopôle, Modèles et expériencesexpériences`expériencesà température nulle, p.47

.. Propriétés-générales-d-'un-vortex, 93 5.1.1 Quantification de la phase, p.95

.. Apparition-des-vortex-dans-le-condensat, 100 5.2.1 Nucléation par augmentation lente de ?, 101 5.2.3 Nucléation, turbulence et dissipation . . . . . . . . . . . . . . . . . . . . . 103

.. Observation-d-'une-ligne-de-vortex-unique, 111 6.1.1 Un réseau de vortex vu de côté : premiers indices 111 6.1.2 Obtention d'une ligne de vortex unique, p.114

.. Vie-et-mort-d-'une-ligne-de-vortex, 119 6.3.1 Evolution dans le temps de la ligne de vortex

.. Mesure-du-moment-cinétique-associéassocié-`-associéà-une-ligne-de-vortex, 121 6.4.1 Modes quadrupolaires et moment cinétique, p.122

.. Condensats-avec-de-nombreux-vortex and .. Un-récipient-cylindrique, 147 8.1.2 Approcher la rotation solide avec des vortex, p.151

.. Introduction-d-'un-terme-quartique-transverse-dans-le-potentiel, 161 9.1.1 Un laser focalisé sur les atomes 161 9.1.2 Potentiel gaussien et termes quartiques, p.165

E. Procédure-expérimentale, 165 9.2.1 Mesure de la nouvelle fréquence transverse 165 9.2.2 Excitation en deux temps par lacuilì ere, p.169

?. Détermination-de and .. Eff-par-trois-méthodes, 169 9.3.1 Détermination de ? eff par les lois d', p.174

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

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

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

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

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

M. Cozzini, S. Stringari, V. Bretin, P. Rosenbusch, and J. Dalibard, Scissors mode of a rotating Bose-Einstein condensate, Physical Review A, vol.67, issue.2, p.21602, 2003.
DOI : 10.1103/PhysRevA.67.021602
URL : https://hal.archives-ouvertes.fr/hal-00002527

V. Bretin, P. Rosenbusch, and J. Dalibard, Dynamics of a single vortex line in a Bose??Einstein condensate, Journal of Optics B: Quantum and Semiclassical Optics, vol.5, issue.2, p.23, 2003.
DOI : 10.1088/1464-4266/5/2/354
URL : https://hal.archives-ouvertes.fr/hal-00002528

V. Bretin, P. Rosenbusch, F. Chevy, G. V. Shlyapnikov, and J. Dalibard, Quadrupole Oscillation of a Single-Vortex Bose-Einstein Condensate: Evidence for Kelvin Modes, Physical Review Letters, vol.90, issue.10, p.100403, 2003.
DOI : 10.1103/PhysRevLett.90.100403
URL : https://hal.archives-ouvertes.fr/hal-00001440

V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Fast Rotation of a Bose-Einstein Condensate, Physical Review Letters, vol.92, issue.5, p.50403, 2004.
DOI : 10.1103/PhysRevLett.92.050403

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

J. D. Miller, R. A. Cline, and D. J. Heinzen, Photoassociation spectrum of ultracold Rb atoms, Physical Review Letters, vol.71, issue.14, p.2204, 1993.
DOI : 10.1103/PhysRevLett.71.2204

H. Marion, F. P. Santos, M. Abgrall, S. Zhang, Y. Sortais et al., Search for Variations of Fundamental Constants using Atomic Fountain Clocks, Physical Review Letters, vol.90, issue.15, p.150801, 2003.
DOI : 10.1103/PhysRevLett.90.150801
URL : https://hal.archives-ouvertes.fr/hal-00002552

J. Söding, D. Guéry-odelin, P. Desbiolles, F. Chevy, H. Inamori et al., Three-body decay of a rubidium Bose???Einstein condensate, Applied Physics B, vol.69, issue.4, pp.257-61, 1999.
DOI : 10.1007/s003400050805

J. Cubizolles, T. Bourdel, S. J. Kokkelmans, G. V. Shlyapnikov, and C. Salomon, Molecules from a Fermi Gas, Physical Review Letters, vol.91, issue.24, p.240401, 2003.
DOI : 10.1103/PhysRevLett.91.240401

S. Dürr, T. Voltz, A. Marte, and G. Rempe, Observation of Molecules Produced from a Bose-Einstein Condensate, Physical Review Letters, vol.92, issue.2, p.20406, 2004.
DOI : 10.1103/PhysRevLett.92.020406

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

C. A. Regal and D. S. Jin, Measurement of Positive and Negative Scattering Lengths in a Fermi Gas of Atoms, Physical Review Letters, vol.90, issue.23, p.230404, 2003.
DOI : 10.1103/PhysRevLett.90.230404

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

M. Greiner, O. Mandel, T. Hänsch, and I. Bloch, Collapse and revival of the matter wave field of a Bose???Einstein condensate, Nature, vol.87, issue.6902, p.51, 2002.
DOI : 10.1103/PHYSREVLETT.86.5188

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. B. Ovchinnikov, J. H. Müller, M. R. Doery, E. J. Vredenbregt, K. Helmerson et al., Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave, Physical Review Letters, vol.83, issue.2, p.284, 1999.
DOI : 10.1103/PhysRevLett.83.284

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

S. Balibar, Looking Back at Superfluid Helium, p.303561, 2003.
DOI : 10.1007/978-3-0348-7932-3_2
URL : https://hal.archives-ouvertes.fr/hal-00000262

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

M. Tinkham, Introduction to superconductivity, 1996.

O. Avenel, P. Hakonen, and E. Varoquaux, Detection of the Rotation of the Earth with a Superfluid Gyrometer, Physical Review Letters, vol.78, issue.19, p.3602, 1997.
DOI : 10.1103/PhysRevLett.78.3602

D. Koelle, R. Kleiner, F. Ludwig, E. Dantsker, and J. Clarke, High-transition-temperature superconducting quantum interference devices, Reviews of Modern Physics, vol.71, issue.3, p.631, 1999.
DOI : 10.1103/RevModPhys.71.631

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

C. Cohen-tannoudji, Condensation de Bose-Einstein des gaz atomiques ultra-froids (effet des interactions, 1998.

C. Cohen-tannoudji, Condensation de Bose-Einstein des gaz atomiques ultra-froids (propriétés de cohérence), 1999.

. Cohen-tannoudji, Condensation de Bose-Einstein des gaz ato- miques ultra-froids (réponse d'un condensatà condensat`condensatà divers types d'excitation, 2000.

C. Cohen-tannoudji, Condensation de Bose-Einstein des gaz atomiques ultra-froids (rotation et modes propres, 2001.

D. Guéry-odelin, Dynamique collisionnelle des gaz d'alcalins lourds : du refroidissementévaporatifà refroidissementévaporatifrefroidissementévaporatif`refroidissementévaporatifà la condensation de Bose-Einstein, 1998.

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, Laser-cooling and trapping neutral atoms, Annales de Physique, vol.10, issue.6, p.721, 1998.
DOI : 10.1051/anphys:01985001006071700

W. Wohlleben, F. Chevy, K. W. Madison, and J. Dalibard, An atom faucet, The European Physical Journal D, vol.15, issue.2, pp.237-244, 2001.
DOI : 10.1007/s100530170171
URL : https://hal.archives-ouvertes.fr/hal-00002533

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

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

E. Hodby, S. A. Hopkins, G. Hechenblaikner, N. L. Smith, and C. J. Foot, Experimental Observation of a Superfluid Gyroscope in a Dilute Bose-Einstein Condensate, Physical Review Letters, vol.91, issue.9, p.90403, 2003.
DOI : 10.1103/PhysRevLett.91.090403

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. M. O-'hara, S. L. Hemmer, M. E. Gehm, S. R. Granade, and J. E. Thomas, Observation of a Strongly Interacting Degenerate Fermi Gas of Atoms, Science, vol.298, issue.5601, p.2179, 2002.
DOI : 10.1126/science.1079107

T. Bourdel, J. Cubizolles, L. Khaykovich, K. M. Magalhães, S. J. Kokkelmans et al., Fermi Gas, Physical Review Letters, vol.91, issue.2, p.20402, 2003.
DOI : 10.1103/PhysRevLett.91.020402
URL : https://hal.archives-ouvertes.fr/hal-00001552

D. Guéry-odelin, Mean-field effects in a trapped gas, Physical Review A, vol.66, issue.3, p.33613, 2002.
DOI : 10.1103/PhysRevA.66.033613

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, G. V. Shlyapnikov, and J. T. Walraven, Bose-Einstein Condensation in Trapped Atomic Gases, Physical Review Letters, vol.76, issue.15, pp.2670-2673, 1996.
DOI : 10.1103/PhysRevLett.76.2670

P. Storey and M. Olshanii, Closed class of hydrodynamical solutions for the collective excitations of a Bose-Einstein condensate, Physical Review A, vol.62, issue.3, p.33604, 2000.
DOI : 10.1103/PhysRevA.62.033604

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, 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

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

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

R. Onofrio, C. Raman, J. M. Vogels, J. R. Abo-shaeer, A. P. Chikkatur et al., Observation of Superfluid Flow in a Bose-Einstein Condensed Gas, Physical Review Letters, vol.85, issue.11, pp.2228-2231, 2000.
DOI : 10.1103/PhysRevLett.85.2228

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

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

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

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

D. Guéry-odelin and S. Stringari, Scissors Mode and Superfluidity of a Trapped Bose-Einstein Condensed Gas, Physical Review Letters, vol.83, issue.22, p.4452, 1999.
DOI : 10.1103/PhysRevLett.83.4452

O. M. Maragò, S. A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner et al., Observation of the Scissors Mode and Evidence for Superfluidity of a Trapped Bose-Einstein Condensed Gas, Physical Review Letters, vol.84, issue.10, pp.256-259, 2000.
DOI : 10.1103/PhysRevLett.84.2056

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

M. Guilleumas and L. P. Pitaevskii, Landau damping of transverse quadrupole oscillations of an elongated Bose-Einstein condensate, Physical Review A, vol.67, issue.5, p.53607, 2003.
DOI : 10.1103/PhysRevA.67.053607

B. Jackson and E. Zaremba, Accidental Suppression of Landau Damping of the Transverse Breathing Mode in Elongated Bose-Einstein Condensates, Physical Review Letters, vol.89, issue.15, p.150402, 2002.
DOI : 10.1103/PhysRevLett.89.150402

Y. Kagan and L. A. Maksimov, The nonlinear damping of Bose-Einstein condensate oscillations at ultra-low temperatures, preprint cond-mat, 212377.

C. Cercignani, The Boltzmann equation and its applications, 1988.
DOI : 10.1007/978-1-4612-1039-9

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

M. Guilleumas and L. P. Pitaevskii, Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps, Physical Review A, vol.61, issue.1, p.13602, 1999.
DOI : 10.1103/PhysRevA.61.013602

M. Rusch and K. Burnett, Mean-field theory for excitations of trapped Bose condensates at finite temperatures, Physical Review A, vol.59, issue.5, p.3851, 1999.
DOI : 10.1103/PhysRevA.59.3851

U. A. Khawaja and H. Stoof, Kinetic theory of collective excitations and damping in Bose-Einstein condensed gases, Physical Review A, vol.62, issue.5, p.53602, 2000.
DOI : 10.1103/PhysRevA.62.053602

S. Giorgini, Collisionless dynamics of dilute Bose gases: Role of quantum and thermal fluctuations, Physical Review A, vol.61, issue.6, p.63615, 2000.
DOI : 10.1103/PhysRevA.61.063615

L. Teidl, A. Csordás, R. Graham, and P. Szépfalusy, Shifts and widths of collective excitations in trapped Bose gases determined by the dielectric formalism, Phys. Rev. A, vol.61, p.43606, 2000.

S. Morgan, A gapless theory of Bose-Einstein condensation in dilute gases at finite temperature, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.33, issue.19, p.3847, 2000.
DOI : 10.1088/0953-4075/33/19/303

Y. Kagan and L. A. Maksimov, The damping of the Bose-condensate oscillations in a trap at zero temperature, Phys. Rev. A, vol.64, p.13606, 2001.

J. E. Williams and A. Griffin, Damping of condensate collective modes due to equilibration with the noncondensate, Physical Review A, vol.63, issue.2, p.23612, 2001.
DOI : 10.1103/PhysRevA.63.023612

J. E. Williams and A. Griffin, Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud, Physical Review A, vol.64, issue.1, p.13606, 2001.
DOI : 10.1103/PhysRevA.64.013606

B. Jackson and E. Zaremba, Finite-Temperature Simulations of the Scissors Mode in Bose-Einstein Condensed Gases, Physical Review Letters, vol.87, issue.10, p.100404, 2001.
DOI : 10.1103/PhysRevLett.87.100404

D. S. Jin, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, Temperature-Dependent Damping and Frequency Shifts in Collective Excitations of a Dilute Bose-Einstein Condensate, Physical Review Letters, vol.78, issue.5, p.764, 1997.
DOI : 10.1103/PhysRevLett.78.764

D. M. Stamper-kurn, H. Miesner, S. Inouye, M. R. Andrews, and W. Ketterle, Collisionless and Hydrodynamic Excitations of a Bose-Einstein Condensate, Physical Review Letters, vol.81, issue.3, pp.500-503, 1998.
DOI : 10.1103/PhysRevLett.81.500

O. Maragò, G. Hechenblaikner, E. Hodby, and C. J. Foot, Temperature Dependence of Damping and Frequency Shifts of the Scissors Mode of a Trapped Bose-Einstein Condensate, Physical Review Letters, vol.86, issue.18, p.3938, 2001.
DOI : 10.1103/PhysRevLett.86.3938

D. Guéry-odelin, F. Zambelli, J. Dalibard, and S. Stringari, Collective oscillations of a classical gas confined in harmonic traps, Physical Review A, vol.60, issue.6, p.4851, 1999.
DOI : 10.1103/PhysRevA.60.4851

E. Hodby, O. M. Maragò, G. Hechenblaikner, and C. J. Foot, Experimental Observation of Beliaev Coupling in a Bose-Einstein Condensate, Physical Review Letters, vol.86, issue.11, p.2196, 2001.
DOI : 10.1103/PhysRevLett.86.2196

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

Y. Kagan and L. A. Maksimov, Relaxation of Bose-condensate oscillations in a mesoscopic system at T=0, Journal of Experimental and Theoretical Physics Letters, vol.78, issue.11, 312642.
DOI : 10.1134/1.1648298

P. O. Fedichev, U. R. Fischer, and A. Recati, Zero-temperature damping of Bose-Einstein condensate oscillations by vortex-antivortex pair creation, Physical Review A, vol.68, issue.1, p.11602, 2003.
DOI : 10.1103/PhysRevA.68.011602

A. Recati, F. Zambelli, and S. Stringari, Overcritical Rotation of a Trapped Bose-Einstein Condensate, Physical Review Letters, vol.86, issue.3, p.377, 2001.
DOI : 10.1103/PhysRevLett.86.377

L. S. Brown and G. Gabrielse, Geonium theory: Physics of a single electron or ion in a Penning trap, Reviews of Modern Physics, vol.58, issue.1, p.233, 1986.
DOI : 10.1103/RevModPhys.58.233

V. Bretin, Etude de la fraction thermique dans les expériences de tourbillons quantiques sur les condensats de Bose-Einstein, 2000.

D. Guéry-odelin, Spinning up and down a Boltzmann gas, Physical Review A, vol.62, issue.3, p.33607, 2000.
DOI : 10.1103/PhysRevA.62.033607

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

M. Edwards, C. W. Clark, P. Pedri, L. Pitaevksii, and S. Stringari, Consequence of Superfluidity on the Expansion of a Rotating Bose-Einstein Condensate, Physical Review Letters, vol.88, issue.7, p.70405, 2002.
DOI : 10.1103/PhysRevLett.88.070405

G. Hechenblaikner, E. Hodby, S. A. Hopkins, O. M. Maragò, and C. J. Foot, Direct Observation of Irrotational Flow and Evidence of Superfluidity in a Rotating Bose-Einstein Condensate, Physical Review Letters, vol.88, issue.7, p.70406, 2002.
DOI : 10.1103/PhysRevLett.88.070406

S. Sinha and Y. Castin, Dynamic Instability of a Rotating Bose-Einstein Condensate, Physical Review Letters, vol.87, issue.19, p.190402, 2001.
DOI : 10.1103/PhysRevLett.87.190402
URL : https://hal.archives-ouvertes.fr/hal-00002093

W. F. Vinen, The detection of a single quantum of circulation in liquid helium II, Proc. Roy. Soc. A260, p.218

E. J. Yarmchuk, M. J. Gordon, and R. E. Packard, Observation of Stationary Vortex Arrays in Rotating Superfluid Helium, Physical Review Letters, vol.43, issue.3, p.214, 1979.
DOI : 10.1103/PhysRevLett.43.214

P. G. Saffman, Vortex dynamics, 1997.

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

A. J. Leggett, Bose-Einstein condensation in the alkali gases, Rev. Mod. Phys, vol.73, p.333, 2001.

A. L. Fetter and A. A. Svidzinsky, Vortices in a trapped dilute Bose-Einstein condensate, Journal of Physics: Condensed Matter, vol.13, issue.12, p.135, 2001.
DOI : 10.1088/0953-8984/13/12/201

D. J. Thouless, P. Ao, and Q. Niu, Transverse Force on a Quantized Vortex in a Superfluid, Physical Review Letters, vol.76, issue.20, p.3758, 1996.
DOI : 10.1103/PhysRevLett.76.3758

E. B. Sonin, Magnus force in superfluids and superconductors, Physical Review B, vol.55, issue.1, p.485, 1997.
DOI : 10.1103/PhysRevB.55.485

S. V. Iordanskii, On the mutual friction between the normal and superfluid components in a rotating bose gas, Annals of Physics, vol.29, issue.3, p.335, 1964.
DOI : 10.1016/0003-4916(64)90001-6

C. Wexler, Magnus and Iordanskii Forces in Superfluids, Physical Review Letters, vol.79, issue.7, p.1321, 1997.
DOI : 10.1103/PhysRevLett.79.1321

G. Baym and E. Chandler, The hydrodynamics of rotating superfluids. I. Zero-temperature, nondissipative theory, Journal of Low Temperature Physics, vol.43, issue.1-2, p.57, 1983.
DOI : 10.1007/BF00681839

B. Damski and K. Sacha, Changes of the topological charge of vortices, Journal of Physics A: Mathematical and General, vol.36, issue.9, p.2339, 2003.
DOI : 10.1088/0305-4470/36/9/311

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

I. Bialynicki-birula, Z. Bialinicki-birula, and C. Sliwa, Motion of vortex lines in quantum mechanics, Physical Review A, vol.61, issue.3, p.32110, 2000.
DOI : 10.1103/PhysRevA.61.032110

K. Kasamatsu, M. Tsubota, and M. Ueda, Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate, Physical Review A, vol.67, issue.3, p.33610, 2003.
DOI : 10.1103/PhysRevA.67.033610

F. Dalfovo and S. Stringari, Shape deformations and angular-momentum transfer in trapped Bose-Einstein condensates, Physical Review A, vol.63, issue.1, p.11601, 2001.
DOI : 10.1103/PhysRevA.63.011601

D. L. Feder, A. A. Svidzinsky, A. L. Fetter, and C. W. Clark, Anomalous Modes Drive Vortex Dynamics in Confined Bose-Einstein Condensates, Physical Review Letters, vol.86, issue.4, p.564, 2001.
DOI : 10.1103/PhysRevLett.86.564

C. Lobo, A. Sinatra, and Y. Castin, Vortex Lattice Formation in Bose-Einstein Condensates, Physical Review Letters, vol.92, issue.2, p.20403, 2004.
DOI : 10.1103/PhysRevLett.92.020403
URL : https://hal.archives-ouvertes.fr/hal-00002442

G. Baym and C. J. Pethick, Ground-State Properties of Magnetically Trapped Bose-Condensed Rubidium Gas, Physical Review Letters, vol.76, issue.1, pp.6-9, 1996.
DOI : 10.1103/PhysRevLett.76.6

F. Dalfovo and S. Stringari, Bosons in anisotropic traps: Ground state and vortices, Physical Review A, vol.53, issue.4, pp.2477-85, 1996.
DOI : 10.1103/PhysRevA.53.2477

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

D. L. Feder, C. W. Clark, and B. I. Schneider, Vortex Stability of Interacting Bose-Einstein Condensates Confined in Anisotropic Harmonic Traps, Physical Review Letters, vol.82, issue.25, p.4956, 1999.
DOI : 10.1103/PhysRevLett.82.4956

M. Krämer, L. Pitaevskii, S. Stringari, and F. Zambelli, Vortex nucleation and quadrupole deformation or a rotating Bose-Einstein condensate, Lasers Physics, vol.12, p.113, 2002.

E. Lundh and P. Ao, Hydrodynamic approach to vortex lifetimes in trapped Bose condensates, Physical Review A, vol.61, issue.6, p.63612, 2000.
DOI : 10.1103/PhysRevA.61.063612

B. P. Anderson, P. C. Haljan, C. E. Wieman, and E. A. Cornell, Vortex Precession in Bose-Einstein Condensates: Observations with Filled and Empty Cores, Phys. Rev. Lett, vol.85, p.2857, 2000.
DOI : 10.1142/9789812813787_0079

P. O. Fedichev and G. V. Shlyapnikov, Dissipative dynamics of a vortex state in a trapped Bose-condensed gas, Physical Review A, vol.60, issue.3
DOI : 10.1103/PhysRevA.60.R1779

J. E. Williams and M. J. Holland, Preparing topological states of a Bose?Einstein condensate, Nature, vol.401, p.568, 1999.

P. C. Haljan, B. P. Anderson, I. Coddington, and E. A. Cornell, Use of Surface-Wave Spectroscopy to Characterize Tilt Modes of a Vortex in a Bose-Einstein Condensate, Physical Review Letters, vol.86, issue.14, p.2922, 2001.
DOI : 10.1103/PhysRevLett.86.2922

A. E. Leanhardt, A. Görlitz, A. P. Chikkatur, D. Kielpinski, Y. Shin et al., Imprinting Vortices in a Bose-Einstein Condensate using Topological Phases, Physical Review Letters, vol.89, issue.19, p.190403, 2002.
DOI : 10.1103/PhysRevLett.89.190403

A. E. Leanhardt, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, Coreless Vortex Formation in a Spinor Bose-Einstein Condensate, Physical Review Letters, vol.90, issue.14, p.140403, 2003.
DOI : 10.1103/PhysRevLett.90.140403

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

J. R. Abo-shaeer, C. Raman, and W. Ketterle, Formation and Decay of Vortex Lattices in Bose-Einstein Condensates at Finite Temperatures, Physical Review Letters, vol.88, issue.7, p.190403, 2002.
DOI : 10.1103/PhysRevLett.88.070409

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

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

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

B. P. Anderson, P. C. Haljan, C. A. Regal, D. L. Feder, L. A. Collins et al., Watching Dark Solitons Decay into Vortex Rings in a Bose-Einstein Condensate, Physical Review Letters, vol.86, issue.14, p.2926, 2001.
DOI : 10.1103/PhysRevLett.86.2926

E. J. Yarmchuk and R. E. Packard, Photographic studies of quantized vortex lines, Journal of Low Temperature Physics, vol.22, issue.5-6, p.479, 1982.
DOI : 10.1007/BF00683912

S. K. Nemirovskii and W. Fiszdon, Chaotic quantized vortices and hydrodynamic processes in superfluid helium, Reviews of Modern Physics, vol.67, issue.1, p.37, 1995.
DOI : 10.1103/RevModPhys.67.37

N. G. Berloff, Interactions of vortices and finite amplitude sound waves in a condensate and their role in the decay of superfluid turbulence, p.401070, 2004.

H. Träuble and U. Essmann, Vortex lattices in superconductors, Phys. Lett, vol.24, p.526, 1967.

R. Blaauwgeers, V. B. Eltsvo, M. Krusius, J. Ruohio, and R. Schanen, Quantized vorticity in superfluid 3 He-A : structure and dynamics, p.9397, 2000.

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

P. Minnhagen, The two-dimensional Coulomb gas, vortex unbinding, and superfluid-superconducting films, Reviews of Modern Physics, vol.59, issue.4, pp.1001-1066, 1987.
DOI : 10.1103/RevModPhys.59.1001

P. O. Fedichev and A. E. Muryshev, Equilibrium properties and dissipative dynamics of vortex arrays in trapped Bose-condensed gases, Physical Review A, vol.65, issue.6, p.61601, 2002.
DOI : 10.1103/PhysRevA.65.061601

O. N. Zhuravlev, A. E. Muryshev, and P. O. Fedichev, Dissipative dynamics of vortex arrays in anisotropic traps, Physical Review A, vol.64, issue.5, p.53601, 2001.
DOI : 10.1103/PhysRevA.64.053601

A. A. Svidzinsky and A. L. Fetter, Dynamics of a vortex in a trapped Bose-Einstein condensate, Physical Review A, vol.62, issue.6, p.63617, 2000.
DOI : 10.1103/PhysRevA.62.063617

J. J. García-ripoll and V. M. Pérez-garcía, Vortex nucleation and hysteresis phenomena in rotating Bose-Einstein condensates, Physical Review A, vol.63, issue.4, p.41603, 2001.
DOI : 10.1103/PhysRevA.63.041603

J. J. García-ripoll and V. M. Pérez-garcía, Vortex bending and tightly packed vortex lattices in Bose-Einstein condensates, Physical Review A, vol.64, issue.5, p.53611, 2001.
DOI : 10.1103/PhysRevA.64.053611

M. Modugno, L. Pricoupenko, and Y. Castin, Bose-Einstein condensates with a bent vortex in rotating traps, The European Physical Journal D, vol.22, issue.2, pp.235-257, 2003.
DOI : 10.1140/epjd/e2003-00015-y
URL : https://hal.archives-ouvertes.fr/hal-00002391

A. Aftalion and T. Riviere, Vortex energy and vortex bending for a rotating Bose-Einstein condensate, Physical Review A, vol.64, issue.4, p.43611, 2001.
DOI : 10.1103/PhysRevA.64.043611
URL : https://hal.archives-ouvertes.fr/hal-00008644

A. Aftalion and R. L. Jerrard, Shape of vortices for a rotating Bose-Einstein condensate, Physical Review A, vol.66, issue.2, 2002.
DOI : 10.1103/PhysRevA.66.023611

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

W. Thomson, 3. Vibrations of a Columnar Vortex., Proceedings of the Royal Society of Edinburgh, vol.10, pp.155-168, 1880.
DOI : 10.1017/S0370164600044151
URL : https://hal.archives-ouvertes.fr/jpa-00217537

R. I. Epstein and G. Baym, Vortex drag and the spin-up time scale for pulsar glitches, The Astrophysical Journal, vol.387, p.276, 1992.
DOI : 10.1086/171079

T. Mizushima, M. Ichioda, and K. Machida, Beliaev Damping and Kelvin Mode Spectroscopy of a Bose-Einstein Condensate in the Presence of a Vortex Line, Physical Review Letters, vol.90, issue.18, p.180401, 2003.
DOI : 10.1103/PhysRevLett.90.180401

J. E. Williams, E. Zaremba, B. Jackson, T. Nikuni, and A. Griffin, Dynamical Instability of a Condensate Induced by a Rotating Thermal Gas, Physical Review Letters, vol.88, issue.7, p.70401, 2002.
DOI : 10.1103/PhysRevLett.88.070401

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

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. Tang, Structure of excited vortices with higher angular momentum in Bose-Einstein condensates, Physical Review A, vol.70, issue.4, p.309487, 2003.
DOI : 10.1103/PhysRevA.70.043626

G. B. Hess, Angular Momentum of Superfluid Helium in a Rotating Cylinder, Physical Review, vol.161, issue.1, p.189, 1967.
DOI : 10.1103/PhysRev.161.189

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

V. K. Tkachenko, Stability of Vortex Lattices, Sov. Phys, Zh. Eksp. Teor. Fiz. 50, pp.1049-1573, 1966.

G. Baym, Tkachenko Modes of Vortex Lattices in Rapidly Rotating Bose-Einstein Condensates, Physical Review Letters, vol.91, issue.11, p.110402, 2003.
DOI : 10.1103/PhysRevLett.91.110402

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

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

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

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

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.

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

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

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

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 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

N. Regnault and T. Jolicoeur, Quantum Hall fractions for spinless bosons, Physical Review B, vol.69, issue.23, p.312248, 2003.
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

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

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.306378, 2003.
DOI : 10.1103/PhysRevA.68.035601

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

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.308325
DOI : 10.1103/PhysRevA.69.043619

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.212419, 2002.
DOI : 10.1088/0953-4075/37/7/074

K. Yang, F. D. Haldane, and E. H. Rezayi, Wigner crystals in the lowest Landau level at low-filling factors, Physical Review B, vol.64, issue.8, p.81301, 2001.
DOI : 10.1103/PhysRevB.64.081301

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

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

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, Giant vortices in combined harmonic and quartic traps, Physical Review A, vol.69, issue.3, p.309668, 2003.
DOI : 10.1103/PhysRevA.69.033608
URL : https://hal.archives-ouvertes.fr/hal-00008635

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

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.401292, 2004.
DOI : 10.1103/PhysRevA.69.053619

Y. Seurin, Condensats de Bose-Einstein en rotation rapide, mémoire de DEA, Rapport de stage d'option scientifique, 2003.

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

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

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

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

H. Saito and M. Ueda, Adiabatic vortex nucleation by Bragg Reflection in a Bose-Einstein condensate, p.401228, 2004.