A. Astrid, . Benjamin, . Blaise, . Capucine, . Claire et al., I thank you. Finally, I thank those friends who I met outside any common institution and with whom I shared so many glasses of wine and enriching conversations: thank you Anne

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. O. 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, p.3969, 1995.
DOI : 10.1103/PhysRevLett.75.3969

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

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

L. D. Landau and V. L. Ginzburg, On the theory of superconductivity, p.1064, 1950.

E. P. Gross, Structure of a quantized vortex in boson systems, Il Nuovo Cimento, vol.8, issue.3, p.454, 1961.
DOI : 10.1007/BF02731494

L. P. Pitaevskii, Vortex lines in an imperfect Bose gas, Sov. Phys, p.451, 1961.

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

A. J. Leggett, Bose-Einstein condensation in the alkali gases: Some fundamental concepts, Reviews of Modern Physics, vol.73, issue.2, p.307, 2001.
DOI : 10.1103/RevModPhys.73.307

]. B. Demarco and D. S. Jin, Onset of Fermi Degeneracy in a Trap Atomic Gas, Science, vol.285, p.5434, 1999.

S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of ultracold atomic Fermi gases, Reviews of Modern Physics, vol.80, issue.4, p.1215, 2008.
DOI : 10.1103/RevModPhys.80.1215

I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. of Mod, Phys, vol.80, p.885, 2008.

R. P. Feynman, Simulating physics with computers, International Journal of Theoretical Physics, vol.21, issue.6-7, p.467, 1982.
DOI : 10.1007/BF02650179

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

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

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

P. Courteille, R. S. Freeland, D. J. Heinzen, F. A. Van-abeelen, and B. J. Verhaar, Observation of a Feshbach Resonance in Cold Atom Scattering, Physical Review Letters, vol.81, issue.1, p.69, 1998.
DOI : 10.1103/PhysRevLett.81.69

S. Inouye, M. R. Andrews, J. Stenger, H. Miesner, D. M. Stamper-kurn et al., Observation of Feshbach resonances in a Bose???Einstein condensate, Nature, vol.77, issue.6672, p.151, 1998.
DOI : 10.1038/32354

E. Tiesinga, B. J. Verhaar, and H. T. Stoof, Threshold and resonance phenomena in ultracold ground-state collisions, Physical Review A, vol.47, issue.5, p.4114, 1993.
DOI : 10.1103/PhysRevA.47.4114

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. 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

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

M. Greiner, O. Mandel, T. Esslinger, T. Hänsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, vol.415, issue.6867, p.39, 2002.
DOI : 10.1038/415039a

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

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

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

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

C. Orzel, A. K. Tuchman, M. Fenselau, M. Yasuda, and M. A. Kasevich, Squeezed States in a Bose-Einstein Condensate, Science, vol.291, issue.5512, p.2386, 2001.
DOI : 10.1126/science.1058149

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

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, p.223, 2005.
DOI : 10.1088/0953-4075/38/3/007

O. Zobay and B. M. Garraway, Two-Dimensional Atom Trapping in Field-Induced Adiabatic Potentials, Physical Review Letters, vol.86, issue.7, p.1195, 2001.
DOI : 10.1103/PhysRevLett.86.1195

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

S. Hofferberth, I. Lesanovsky, B. Fischer, T. Schumm, and J. Schmiedmayer, Non-equilibrium coherence dynamics in one-dimensional Bose gases, Nature, vol.78, issue.7160, p.324, 2007.
DOI : 10.1038/nature06149

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

I. B. Spielman, W. D. Phillips, and J. V. Porto, Mott-Insulator Transition in a Two-Dimensional Atomic Bose Gas, Physical Review Letters, vol.98, issue.8, p.80404, 2007.
DOI : 10.1103/PhysRevLett.98.080404

Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, Berezinskii???Kosterlitz???Thouless crossover in a trapped atomic gas, Nature, vol.39, issue.7097, p.1118, 2006.
DOI : 10.1038/nature04851

URL : https://hal.archives-ouvertes.fr/hal-00067716

P. Krüger, Z. Hadzibabic, and J. Dalibard, Critical Point of an Interacting Two-Dimensional Atomic Bose Gas, Physical Review Letters, vol.99, issue.4, p.40402, 2007.
DOI : 10.1103/PhysRevLett.99.040402

P. Cladé, C. Ryu, A. Ramanathan, K. Helmerson, and W. D. Phillips, Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid, Physical Review Letters, vol.102, issue.17, p.170401, 2009.
DOI : 10.1103/PhysRevLett.102.170401

M. Cheneau, Transition BKT et potentiels géométriques dans le gaz de Bose bidimensionnel, 2009.

N. Prokof-'ev and B. Svistunov, Two-dimensional weakly interacting Bose gas in the fluctuation region, Phys. Rev. A, vol.66, p.43608, 2002.

M. Holzmann and W. Krauth, Kosterlitz-Thouless Transition of the Quasi-Two-Dimensional Trapped Bose Gas, Physical Review Letters, vol.100, issue.19, p.190402, 2008.
DOI : 10.1103/PhysRevLett.100.190402

M. Greiner, I. Bloch, T. W. Hänsch, and T. Esslinger, Magnetic transport of trapped cold atoms over a large distance, Physical Review A, vol.63, issue.3, p.31401, 2001.
DOI : 10.1103/PhysRevA.63.031401

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Trapping of Neutral Sodium Atoms with Radiation Pressure, Physical Review Letters, vol.59, issue.23, p.2631, 1987.
DOI : 10.1103/PhysRevLett.59.2631

C. G. Townsend, N. H. Edwards, C. J. Cooper, K. P. Zetie, C. J. Foot et al., Phase-space density in the magneto-optical trap, Physical Review A, vol.52, issue.2, p.1423, 1995.
DOI : 10.1103/PhysRevA.52.1423

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould et al., Observation of Atoms Laser Cooled below the Doppler Limit, Physical Review Letters, vol.61, issue.2, p.169, 1988.
DOI : 10.1103/PhysRevLett.61.169

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

F. Schreck, Mixtures of ultracold gases: Fermi sea and Bose-Einstein condensate of lithium isotopes, Annales de Physique, vol.28, issue.2, 2002.
DOI : 10.1051/anphys:2003004

URL : https://hal.archives-ouvertes.fr/tel-00001340

S. P. Rath, Towards a new generation BEC experiment, p.internship report, 2006.

P. Horowitz and W. Hill, The art of electronics, 1989.

W. Petrich, M. H. Anderson, J. R. Ensher, and E. A. Cornell, Stable, Tightly Confining Magnetic Trap for Evaporative Cooling of Neutral Atoms, Physical Review Letters, vol.74, issue.17, p.3352, 1995.
DOI : 10.1103/PhysRevLett.74.3352

M. Mewes, M. R. Andrews, N. J. Van-druten, D. M. Kurn, D. S. Durfee et al., Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap, Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap, p.416, 1996.
DOI : 10.1103/PhysRevLett.77.416

M. D. Barrett, J. A. Sauer, and M. S. Chapman, All-Optical Formation of an Atomic Bose-Einstein Condensate, Physical Review Letters, vol.87, issue.1, p.10404, 2001.
DOI : 10.1103/PhysRevLett.87.010404

L. D. Landau, Theory of energy transfer II, Phys, Z. Sowjetunion, vol.2, p.46, 1932.

C. Zener, Non-Adiabatic Crossing of Energy Levels, Proc. R. Soc. London, p.696, 1932.
DOI : 10.1098/rspa.1932.0165

R. Franzosi, B. Zambon, and E. Arimondo, Nonadiabatic effects in the dynamics of atoms confined in a cylindric time-orbiting-potential magnetic trap, Physical Review A, vol.70, issue.5, p.53603, 2004.
DOI : 10.1103/PhysRevA.70.053603

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, p.1706, 1999.
DOI : 10.1126/science.283.5408.1706

J. H. Müller, D. Ciampini, O. Morsch, G. Smirne, M. Fazzi et al., Bose-Einstein condensation of rubidium atoms in a triaxial TOP trap, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.33, issue.19, p.4095, 2000.
DOI : 10.1088/0953-4075/33/19/320

E. Hodby, G. Hechenblaikner, O. M. Marago, J. Arlt, S. Hopkins et al., Bose-Einstein condensation in a stiff TOP trap with adjustable geometry, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.33, issue.19, p.4087, 2000.
DOI : 10.1088/0953-4075/33/19/319

F. G. Major and H. G. Dehmelt, Exchange-Collision Technique for the rf Spectroscopy of Stored Ions, Physical Review, vol.170, issue.1, p.91, 1968.
DOI : 10.1103/PhysRev.170.91

R. V. Lovelace, T. J. Mehanian, T. J. Tommila, and D. M. Lee, Magnetic confinement of a neutral gas, Nature, vol.44, issue.110, p.30, 1985.
DOI : 10.1038/318030a0

R. V. Lovelace and T. J. Tommila, Theory of Bose-Einstein condensation of atomic hydrogen in a dynamic trap, Physical Review A, vol.35, issue.9, p.3597, 1987.
DOI : 10.1103/PhysRevA.35.3597

E. A. Cornell, C. Monroe, and C. E. Wieman, Multiply loaded, ac magnetic trap for neutral atoms, Physical Review Letters, vol.67, issue.18, p.2439, 1991.
DOI : 10.1103/PhysRevLett.67.2439

S. Gov and S. Shtrikman, Dynamic stability of the time-averaged orbiting potential trap: Exact classical analysis, Journal of Applied Physics, vol.86, issue.4, p.2250, 1999.
DOI : 10.1063/1.371038

J. H. Müller, O. Morsch, D. Ciampini, M. Anderlini, R. Mannella et al., Atomic Micromotion and Geometric Forces in a Triaxial Magnetic Trap, Physical Review Letters, vol.85, issue.21, p.4454, 2000.
DOI : 10.1103/PhysRevLett.85.4454

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, p.806, 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

J. Arlt, O. Marago, E. Hodby, S. A. Hopkins, G. Hechenblaikner et al., Bose-Einstein condensation in a rotating anisotropic TOP trap, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.32, issue.24, p.5861, 1999.
DOI : 10.1088/0953-4075/32/24/320

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, 2001.
DOI : 10.1103/PhysRevLett.88.010405

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

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

N. V. Vitanov and K. Suominen, Time-dependent control of ultracold atoms in magnetic traps, Physical Review A, vol.56, issue.6, p.4377, 1997.
DOI : 10.1103/PhysRevA.56.R4377

O. Morizot, C. L. Alzar, P. Pottie, V. Lorent, and H. Perrin, Trapping and cooling of rf-dressed atoms in a quadrupole magnetic field, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.40, issue.20, p.4013, 2007.
DOI : 10.1088/0953-4075/40/20/004

URL : https://hal.archives-ouvertes.fr/hal-00173059

T. Schumm, S. Hofferberth, L. M. Andersson, S. Zildermuth, 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. Hofferberth, I. Lesanovsky, T. Schumm, A. Imambekov, V. Gritsev et al., Probing quantum and thermal noise in an interacting many-body system, Nature Physics, vol.0701, issue.6, p.489, 2008.
DOI : 10.1038/nphys941

I. Lesanovsky and W. Von-klitzing, Time-Averaged Adiabatic Potentials: Versatile Matter-Wave Guides and Atom Traps, Physical Review Letters, vol.99, issue.8, p.83001, 2007.
DOI : 10.1103/PhysRevLett.99.083001

S. Hofferberth, B. Fischer, T. Schumm, J. Schmiedmayer, and I. Lesanovsky, Ultracold atoms in radio-frequency dressed potentials beyond the rotating-wave approximation, Physical Review A, vol.76, issue.1, p.13401, 2007.
DOI : 10.1103/PhysRevA.76.013401

R. K. Easwaran, L. Longchambon, P. Pottie, V. Lorent, H. Perrin et al., RF spectroscopy in a resonant RF-dressed trap, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.43, issue.6, p.65302, 2010.
DOI : 10.1088/0953-4075/43/6/065302

URL : https://hal.archives-ouvertes.fr/hal-00456214

F. Chevy, V. Bretin, P. Rosenbusch, K. W. 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

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

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

M. Mewes, M. R. Andrews, N. J. Van-druten, D. M. Kurn, D. S. Durfee et al., Collective Excitations of a Bose-Einstein Condensate in a Magnetic Trap, Physical Review Letters, vol.77, issue.6, p.988, 1996.
DOI : 10.1103/PhysRevLett.77.988

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

M. Edwards, P. A. Ruprecht, K. Burnett, R. J. Dodd, and C. W. Clark, Collective Excitations of Atomic Bose-Einstein Condensates, Physical Review Letters, vol.77, issue.9, p.1671, 1996.
DOI : 10.1103/PhysRevLett.77.1671

P. A. Ruprecht, M. Edwards, K. Burnett, and C. W. Clark, Probing the linear and nonlinear excitations of Bose-condensed neutral atoms in a trap, Physical Review A, vol.54, issue.5, p.4178, 1996.
DOI : 10.1103/PhysRevA.54.4178

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, p.500, 1998.
DOI : 10.1103/PhysRevLett.81.500

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

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

C. E. Wieman, D. E. Pritchard, and D. J. Wineland, Atom cooling, trapping, and quantum manipulation, Reviews of Modern Physics, vol.71, issue.2, p.253, 1999.
DOI : 10.1103/RevModPhys.71.S253

P. Lemonde, O. Morice, E. Peik, J. Reichel, H. Perrin et al., An Opto-electric Trap for Cold Atoms, Europhysics Letters (EPL), vol.32, issue.7, p.555, 1995.
DOI : 10.1209/0295-5075/32/7/003

P. Krüger, X. Luo, M. W. Klein, K. Brugger, A. Haase et al., Trapping and Manipulating Neutral Atoms with Electrostatic Fields, Physical Review Letters, vol.91, issue.23, p.233201, 2003.
DOI : 10.1103/PhysRevLett.91.233201

R. J. Spreeuw, C. Gerz, L. S. Goldner, W. D. Phillips, S. L. Rolston et al., Demonstration of neutral atom trapping with microwaves, Physical Review Letters, vol.72, issue.20, p.3162, 1994.
DOI : 10.1103/PhysRevLett.72.3162

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate, Optics Communications, vol.127, issue.4-6, p.183, 1996.
DOI : 10.1016/0030-4018(96)00070-3

]. J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark, L. A. Collins et al., Generating Solitons by Phase Engineering of a Bose-Einstein Condensate, Science, vol.287, issue.5450, p.97, 2000.
DOI : 10.1126/science.287.5450.97

N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-dunlop, and M. J. Wegener, Laser beams with phase singularities, Optical and Quantum Electronics, vol.33, issue.9, p.951, 1992.
DOI : 10.1007/BF01588597

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, High-order Laguerre???Gaussian laser modes for studies of cold atoms, Optics Communications, vol.156, issue.4-6, p.300, 1998.
DOI : 10.1016/S0030-4018(98)00464-7

E. R. Dufresne and D. G. Grier, Optical tweezer arrays and optical substrates created with diffractive optics, Review of Scientific Instruments, vol.69, issue.5, p.1974, 1998.
DOI : 10.1063/1.1148883

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Computer-generated holographic optical tweezer arrays, Review of Scientific Instruments, vol.72, issue.3, p.1810, 2001.
DOI : 10.1063/1.1344176

URL : http://arxiv.org/abs/cond-mat/0008414

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys et al., Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator, Journal of the Optical Society of America B, vol.21, issue.11, p.1889, 2004.
DOI : 10.1364/JOSAB.21.001889

J. P. Gordon and A. Ashkin, Motion of atoms in a radiation trap, Physical Review A, vol.21, issue.5, p.1606, 1980.
DOI : 10.1103/PhysRevA.21.1606

F. Bloch and A. Siegert, Magnetic Resonance for Nonrotating Fields, Physical Review, vol.57, issue.6, p.522, 1940.
DOI : 10.1103/PhysRev.57.522

R. Grimm, W. M. , and Y. B. Ovchinnikov, Optical Dipole Traps for Neutral Atoms, Advances in atomic, molecular, and optical physics, 2000.
DOI : 10.1016/S1049-250X(08)60186-X

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 1999.
DOI : 10.1017/CBO9781139644181

A. E. Siegman, Defining, measuring, and optimizing laser beam quality, Proc. SPIE, pp.2-12, 1993.

E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, Hypergeometric-Gaussian modes, Optics Letters, vol.32, issue.21, p.3053, 2007.
DOI : 10.1364/OL.32.003053

A. Posazhennikova, : Weakly interacting, dilute Bose gases in 2D, Reviews of Modern Physics, vol.78, issue.4, p.1111, 2006.
DOI : 10.1103/RevModPhys.78.1111

Z. Hadzibabic and J. Dalibard, Two-dimensional Bose fluids: An atomic physics perspective, Nano optics and atomics: transport of light and matter waves, 2009.

R. E. Peierls, Quelques propriétés typiques des corps solides, Ann. Inst. Henri Poincaré, vol.5, p.177, 1935.

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.26, p.1307, 1966.
DOI : 10.1103/PhysRevLett.17.1307

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

V. L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimension system possessing a continuous symmetry group -ii. Quantum systems, Sov. Phys. JETP, vol.34, p.610, 1971.

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

D. J. Bishop and J. D. Reppy, films, Physical Review B, vol.22, issue.11, p.5171, 1980.
DOI : 10.1103/PhysRevB.22.5171

C. Leemann, P. Lerch, G. A. Racine, and P. Martinoli, Vortex Dynamics and Phase Transitions in a Two-Dimensional Array of Josephson Junctions, Physical Review Letters, vol.56, issue.12, p.1291, 1986.
DOI : 10.1103/PhysRevLett.56.1291

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

V. Schweikhard, S. Tung, and E. A. Cornell, Vortex Proliferation in the Berezinskii-Kosterlitz-Thouless Regime on a Two-Dimensional Lattice of Bose-Einstein Condensates, Physical Review Letters, vol.99, issue.3, p.30401, 2007.
DOI : 10.1103/PhysRevLett.99.030401

M. Holzmann, M. Chevallier, and W. Krauth, Semiclassical theory of the quasi???two-dimensional trapped Bose gas, EPL (Europhysics Letters), vol.82, issue.3, p.30001, 2008.
DOI : 10.1209/0295-5075/82/30001

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 and G. V. Shlyapnikov, Interatomic collisions in a tightly confined Bose gas, Physical Review A, vol.64, issue.1, p.12706, 2001.
DOI : 10.1103/PhysRevA.64.012706

URL : https://hal.archives-ouvertes.fr/hal-00002133

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

S. N. Bose, Planck???s law and the light quantum hypothesis, Journal of Astrophysics and Astronomy, vol.15, issue.1, p.178, 1924.
DOI : 10.1007/BF03010400

O. Penrose and L. Onsager, Bose-Einstein Condensation and Liquid Helium, Physical Review, vol.104, issue.3, p.576, 1956.
DOI : 10.1103/PhysRev.104.576

S. T. Bramwell and P. C. Holdsworth, Magnetization: A characteristic of the Kosterlitz-Thouless-Berezinskii transition, Physical Review B, vol.49, issue.13, p.8811, 1994.
DOI : 10.1103/PhysRevB.49.8811

Z. Hadzibabic, P. Krüger, M. Cheneau, S. P. Rath, and J. Dalibard, The trapped twodimensional Bose gas: from Bose?Einstein condensation to Berezinskii?Kosterlitz?Thouless physics, New J. Phys, vol.10, p.4500, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00194992

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Fölling et al., Two-dimensional quantum gas in a hybrid surface trap, Physical Review A, vol.80, issue.2, p.21602, 2009.
DOI : 10.1103/PhysRevA.80.021602

D. S. Petrov, G. V. Gangardt, and G. V. Shlyapnikov, Low-dimensional trapped gases, Journal de Physique IV (Proceedings), vol.116, issue.3, 2004.
DOI : 10.1051/jp4:2004116001

URL : https://hal.archives-ouvertes.fr/hal-00003349

M. Holzmann, On the mean-field formula of the Kosterlitz-Thouless-Berezinskii transition temperature of a trapped two dimensional Bose gas

M. Holzmann, G. Baym, J. Blaizot, and F. Laloë, Superfluid transition of homogeneous and trapped two-dimensional Bose gases, Proceedings of the National Academy of Sciences, vol.104, issue.5, p.1476, 2007.
DOI : 10.1073/pnas.0609957104

R. K. Bhaduri, S. M. Reimann, S. Viefers, A. G. Choudhury, and M. K. Srivastava, The effect of interactions on Bose-Einstein condensation in a quasi two-dimensional harmonic trap, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.33, issue.19, p.3895, 2000.
DOI : 10.1088/0953-4075/33/19/304

R. N. Bisset, D. Baillie, and P. B. Blakie, Analysis of the Holzmann-Chevallier-Krauth theory for the trapped quasi-two-dimensional Bose gas, Physical Review A, vol.79, issue.1, p.13602, 2009.
DOI : 10.1103/PhysRevA.79.013602

M. Holzmann, M. Chevallier, and W. Krauth, Universal correlations and coherence in quasi-two-dimensional trapped Bose gases, arXiv 0911, p.1704, 2009.

A. Y. Cherny and A. A. Shanenko, Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation, Physical Review E, vol.64, issue.2, p.27105, 2001.
DOI : 10.1103/PhysRevE.64.027105

L. Pricoupenko, Variational approach for the two-dimensional trapped Bose-Einstein condensate, Physical Review A, vol.70, issue.1, p.13601, 2004.
DOI : 10.1103/PhysRevA.70.013601

URL : https://hal.archives-ouvertes.fr/hal-00000582

C. Mora and Y. Castin, Ground State Energy of the Two-Dimensional Weakly Interacting Bose Gas: First Correction Beyond Bogoliubov Theory, Physical Review Letters, vol.102, issue.18, p.180404, 2009.
DOI : 10.1103/PhysRevLett.102.180404

URL : https://hal.archives-ouvertes.fr/hal-00384876

S. Pilati, J. Boronat, J. Casulleras, and S. Giorgini, Quantum Monte Carlo simulation of a two-dimensional Bose gas, Physical Review A, vol.71, issue.2, p.23605, 2005.
DOI : 10.1103/PhysRevA.71.023605

G. E. Astrakharchik, J. Boronat, J. Casulleras, I. L. Kurbakov, and Y. E. Lozovik, Equation of state of a weakly interacting two-dimensional Bose gas studied at zero temperature by means of quantum Monte Carlo methods, Physical Review A, vol.79, issue.5, p.51602, 2009.
DOI : 10.1103/PhysRevA.79.051602

P. J. Price, Density Fluctuations at Low Temperatures, Physical Review, vol.94, issue.2, p.257, 1954.
DOI : 10.1103/PhysRev.94.257

S. Giorgini, L. P. Pitaevskii, and S. Stringari, Anomalous Fluctuations of the Condensate in Interacting Bose Gases, Anomalous Fluctuations of the Condensate in Interacting Bose Gases, p.5040, 1998.
DOI : 10.1103/PhysRevLett.80.5040

G. E. Astrakharchik, R. Combescot, and L. P. Pitaevskii, Fluctuations of the number of particles within a given volume in cold quantum gases, Physical Review A, vol.76, issue.6, p.63616, 2007.
DOI : 10.1103/PhysRevA.76.063616

F. Schlögl and E. Schöll, A relation between cumulants of a thermodynamic variable and the state equation, Zeitschrift f???r Physik B Condensed Matter, vol.17, issue.1, p.61, 1983.
DOI : 10.1007/BF01304045

Y. Kagan, E. L. Surkov, and G. V. Shlyapnikov, Evolution of a Bose gas in anisotropic time-dependent traps, Physical Review A, vol.55, issue.1, p.18, 1997.
DOI : 10.1103/PhysRevA.55.R18

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

B. Gao, Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: Analytic results, Physical Review A, vol.48, issue.3, p.2443, 1993.
DOI : 10.1103/PhysRevA.48.2443

C. C. Bradley, C. A. Sackett, and R. G. Hulet, Analysis of in situ images of Bose-Einstein condensates of lithium, Physical Review A, vol.55, issue.5, p.3951, 1997.
DOI : 10.1103/PhysRevA.55.3951

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, p.257, 1999.
DOI : 10.1007/s003400050805

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

O. Morice, Y. Castin, and J. Dalibard, Refractive index of a dilute Bose gas, Physical Review A, vol.51, issue.5, p.3896, 1995.
DOI : 10.1103/PhysRevA.51.3896

]. E. Mandonnet, Etude théorique d'un gaz de Bose ultra-froid : 1. Diffusion et localisation de la lumière 2, 2000.

H. D. Politzer, Bose-stimulated scattering off a cold atom trap, Physical Review A, vol.55, issue.2, p.1140, 1997.
DOI : 10.1103/PhysRevA.55.1140

G. Reinaudi, T. Lahaye, Z. Wang, and D. Guéry-odelin, Strong saturation absorption imaging of dense clouds of ultracold atoms, Optics Letters, vol.32, issue.21, p.3143, 2007.
DOI : 10.1364/OL.32.003143

R. J. Noll, Zernike polynomials and atmospheric turbulence*, Journal of the Optical Society of America, vol.66, issue.3, p.207, 1976.
DOI : 10.1364/JOSA.66.000207

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, p.637, 1997.
DOI : 10.1126/science.275.5300.637

A. Polkovnikov, E. Altman, and E. Demler, Interference between independent fluctuating condensates, Proceedings of the National Academy of Sciences, vol.103, issue.16, p.6125, 2006.
DOI : 10.1073/pnas.0510276103

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1458842

V. Gritsev, E. Altman, E. Demler, and A. Polkovnikov, Full quantum distribution of contrast in interference experiments between interacting one-dimensional Bose liquids, Nature Physics, vol.318, issue.10, p.705, 2006.
DOI : 10.1016/S0370-1573(99)00062-9

Z. Hadzibabic, P. Krüger, and J. Dalibard, Interference contrasts between two quasi-twodimensional Bose gases

A. A. Burkov, M. D. Lukin, and E. Demler, Decoherence Dynamics in Low-Dimensional Cold Atom Interferometers, Physical Review Letters, vol.98, issue.20, p.200404, 2007.
DOI : 10.1103/PhysRevLett.98.200404

C. A. Mead and D. G. Truhlar, On the determination of Born???Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei, The Journal of Chemical Physics, vol.70, issue.5, p.2284, 1979.
DOI : 10.1063/1.437734

M. V. Berry, Geometric Phases in Physics, chap. The quantum phase, five years after, World Scientific, pp.7-28, 1989.

J. Moody, A. Shapere, and F. Wilczek, Geometric Phase in Physics, chap. Adiabatic Effective Lagrangians, World Scientific, pp.160-183, 1989.

A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, and J. Zwanziger, The Geometric Phase in Quantum Systems, 2003.
DOI : 10.1007/978-3-662-10333-3

M. V. Berry, Quantal Phase Factors Accompanying Adiabatic Changes, Proc. R. Soc. Lond, p.45, 1984.
DOI : 10.1098/rspa.1984.0023

G. Juzeli¯-unas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, Light-induced effective magnetic fields for ultracold atoms in planar geometries, Physical Review A, vol.73, issue.2, p.25602, 2006.
DOI : 10.1103/PhysRevA.73.025602

M. Cheneau, S. P. Rath, T. Yefsah, K. J. Günter, G. Juzeli¯-unas et al., Geometric potentials in quantum optics: A semi-classical interpretation, EPL (Europhysics Letters), vol.83, issue.6, p.60001, 2008.
DOI : 10.1209/0295-5075/83/60001

URL : https://hal.archives-ouvertes.fr/hal-00306182

K. J. Günter, M. Cheneau, T. Yefsah, S. P. Rath, and J. Dalibard, Practical scheme for a light-induced gauge field in an atomic Bose gas, Physical Review A, vol.79, issue.1, p.11604, 2009.
DOI : 10.1103/PhysRevA.79.011604

Y. Lin, R. L. Compton, A. R. Perry, W. D. Phillips, J. V. Porto et al., Bose-Einstein Condensate in a Uniform Light-Induced Vector Potential, Bose-Einstein Condensate in a Uniform Light-Induced Vector Potential, p.130401, 2009.
DOI : 10.1103/PhysRevLett.102.130401

Y. Lin, R. L. Compton, K. Jiménez-garcía, J. V. Porto, and I. B. Spielman, Synthetic magnetic fields for ultracold neutral atoms, Nature, vol.57, issue.7273, p.628, 2009.
DOI : 10.1038/nature08609