L. D. Landau and E. M. Lifshitz, Statistical Physics, 1980.

P. Mohn, Magnetism in the Solid State, 2005.

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

J. G. Daunt and R. S. Smith, The Problem of Liquid Helium???Some Recent Aspects, Reviews of Modern Physics, vol.91, issue.2, pp.172-236, 1954.
DOI : 10.1103/RevModPhys.26.172

. Satyendra-nath-bose, Plancks Gesetz und Lichtquantenhypothese, Zeitschrift f???r Physik, vol.26, issue.1, p.178, 1924.
DOI : 10.1007/BF01327326

A. Einstein, Quantentheorie des einatomigen idealen Gases, Preussische Akademie der Wissenschaten, 1924.
DOI : 10.1002/3527608958.ch27

S. Chu, Nobel Lecture: The manipulation of neutral particles, Reviews of Modern Physics, vol.20, issue.3, pp.685-706, 1998.
DOI : 10.1103/RevModPhys.70.685

W. D. Phillips, Nobel Lecture: Laser cooling and trapping of neutral atoms, Reviews of Modern Physics, vol.67, issue.3, pp.721-741, 1998.
DOI : 10.1103/RevModPhys.70.721

C. N. Cohen-tannoudji, Nobel Lecture: Manipulating atoms with photons, Reviews of Modern Physics, vol.35, issue.3, pp.707-719, 1998.
DOI : 10.1103/RevModPhys.70.707

W. Ketterle, Nobel lecture: When atoms behave as waves: Bose-Einstein condensation and the atom laser, Reviews of Modern Physics, vol.43, issue.4, pp.1131-1151, 2002.
DOI : 10.1103/RevModPhys.74.1131

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

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.40, issue.3, pp.875-893, 2002.
DOI : 10.1103/RevModPhys.74.875

B. Kendall, M. Davis, . Mewes, R. Michael, . Andrews et al., Bose-einstein condensation in a gas of sodium atoms, Physical review letters, issue.22, p.753969, 1995.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Reviews of Modern Physics, vol.32, issue.3, p.463, 1999.
DOI : 10.1103/RevModPhys.71.463

I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Reviews of Modern Physics, vol.91, issue.196, pp.885-964, 2008.
DOI : 10.1103/PhysRevLett.92.120403

URL : https://hal.archives-ouvertes.fr/hal-00195515

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, issue.6672, pp.392-151, 1998.

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Reviews of Modern Physics, vol.55, issue.2, pp.1225-1286, 2010.
DOI : 10.1103/PhysRevLett.92.120403

M. R. Andrews, Observation of Interference Between Two Bose Condensates, Science, vol.275, issue.5300, pp.637-641, 1997.
DOI : 10.1126/science.275.5300.637

T. Esslinger, I. Bloch, and T. W. Hänsch, Measurement of the spatial coherence of a trapped bose gas at the phase transition, Nature, issue.6766, pp.403166-170, 2000.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman et al., Vortices in a bose-einstein condensate, Physical Review Letters, issue.13, pp.832498-2501, 1999.
DOI : 10.1142/9789812813787_0077

URL : http://arxiv.org/abs/cond-mat/9908209

K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Vortex Formation in a Stirred Bose-Einstein Condensate, Physical Review Letters, vol.58, issue.5, pp.806-809, 2000.
DOI : 10.1103/PhysRevLett.84.806

J. R. Abo-shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of Vortex Lattices in Bose-Einstein Condensates, Science, vol.292, issue.5516, pp.292476-479, 2001.
DOI : 10.1126/science.1060182

C. Raman, M. Köhl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz et al., Evidence for a Critical Velocity in a Bose-Einstein Condensed Gas, Physical Review Letters, vol.83, issue.13, pp.832502-2505, 1999.
DOI : 10.1103/PhysRevLett.83.2502

B. Demarco, S. Deborah, and . Jin, Onset of Fermi Degeneracy in a Trapped Atomic Gas, Science, vol.285, issue.5434, pp.1703-1706, 1999.
DOI : 10.1126/science.285.5434.1703

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

B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling et al., Tonks?girardeau gas of ultracold atoms in an optical lattice, Nature, issue.6989, pp.429277-281, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00009247

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, pp.4411118-1121, 2006.
DOI : 10.1038/nature04851

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

R. Desbuquois, L. Chomaz, T. Yefsah, J. Léonard, J. Beugnon et al., Superfluid behaviour of a two-dimensional Bose gas, Nature Physics, vol.62, issue.9, pp.645-648, 2012.
DOI : 10.1103/PhysRevLett.106.130401

F. Gerbier, J. H. Hywissen, S. Richard, M. Hugbart, P. Bouyer et al., Critical Temperature of a Trapped, Weakly Interacting Bose Gas, Physical Review Letters, vol.109, issue.3, p.30405, 2004.
DOI : 10.1103/PhysRevLett.88.093201

URL : https://hal.archives-ouvertes.fr/hal-00000490

M. Greiner, O. Mandel, T. Esslinger, H. W. Hänsch, and I. Bloch, Quantum phase transition from a superluid to a mott insulator in a gas of ultracold atoms, Nature, issue.6867, pp.41539-41583, 2002.

I. Spielman, W. Phillips, and J. Porto, Mott-Insulator Transition in a Two-Dimensional Atomic Bose Gas, Physical Review Letters, vol.34, issue.8, p.98, 2007.
DOI : 10.1103/PhysRevA.73.051601

H. Hilo-stöferle, C. Moritz, M. Schori, T. Köhl, and . Esslinger, Transition from a strongly interacting 1d superluid to a mott insulator, Physical Review Letters, issue.13, p.92, 2004.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht et al., Direct observation of Anderson localization of matter waves in a controlled disorder, Nature, vol.100, issue.7197, pp.453891-894, 2008.
DOI : 10.1038/nature07000

URL : https://hal.archives-ouvertes.fr/hal-00271681

M. Boll, T. A. Hilker, G. Salomon, A. Omran, J. Nespolo et al., Spin- and density-resolved microscopy of antiferromagnetic correlations in Fermi-Hubbard chains, Science, vol.43, issue.9, pp.3531257-1260, 2016.
DOI : 10.1103/PhysRevLett.104.090402

L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang et al., Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model, Science, vol.33, issue.1, pp.3531260-1264, 2016.
DOI : 10.1103/PhysRevB.40.506

D. M. Stamper-kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye, H. Miesner et al., Optical coninement of a bose-einstein condensate, Physical Review Letters, issue.10, pp.802027-2030, 1998.

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, Optical Dipole Traps for Neutral Atoms, Advances in Atomic, Molecular and Optical Physics, vol.42, pp.95-170, 2000.
DOI : 10.1016/S1049-250X(08)60186-X

URL : http://arxiv.org/abs/physics/9902072

D. Vollhardt and P. W. Ölle, he Superluid Phases of Helium 3, 1990.
DOI : 10.1063/1.2810215

H. Schmaljohann, M. Erhard, J. Kronjäger, M. Kottke, S. Van-staa et al., Spinor Bose-Einstein Condensates, Physical Review Letters, vol.67, issue.4, p.40402, 2004.
DOI : 10.1007/s003400050805

H. Schmaljohann, M. Erhard, J. Kronjäger, K. Sengstock, and K. Bongs, Dynamics and thermodynamics in spinor quantum gases, Applied Physics B, vol.91, issue.8, pp.1001-1007, 2004.
DOI : 10.1007/s00340-004-1664-6

H. Schmaljohann, M. Erhard, J. Kronjägert, M. Kottke, S. Van-staa et al., Magnetism in ultracold quantum gases, Journal of Modern Optics, vol.51, issue.12, pp.51-1829, 2004.
DOI : 10.1007/s00340-003-1334-0

J. Kronjäger, C. Becker, . Brinkmann, P. Walser, . Navez et al., Evolution of a spinor condensate: Coherent dynamics, dephasing, and revivals, Physical Review A, vol.72, issue.6, p.72063619, 2005.
DOI : 10.1038/nphys153

W. Zhang, D. L. Zhou, M. Chang, M. S. Chapman, and L. You, Coherent spin mixing dynamics in a spin-1 atomic condensate, Physical Review A, vol.72, issue.1, p.13602, 2005.
DOI : 10.1103/PhysRevLett.78.2511

URL : http://arxiv.org/abs/cond-mat/0502061

H. Pu, C. K. Law, S. Raghavan, J. H. Eberly, and N. P. Bigelow, Spin-mixing dynamics of a spinor Bose-Einstein condensate, Physical Review A, vol.55, issue.2, pp.1463-1470, 1999.
DOI : 10.1103/PhysRevA.60.1463

C. K. Law, H. Pu, and N. P. Bigelow, Quantum Spins Mixing in Spinor Bose-Einstein Condensates, Physical Review Letters, vol.81, issue.24, p.5257, 1998.
DOI : 10.1103/PhysRevLett.81.5257

URL : http://arxiv.org/abs/cond-mat/9807258

Y. Liu, S. Jung, S. E. Maxwell, L. D. Turner, E. Tiesinga et al., Quantum Phase Transitions and Continuous Observation of Spinor Dynamics in an Antiferromagnetic Condensate, Physical Review Letters, vol.102, issue.12, p.125301, 2009.
DOI : 10.1016/S0375-9601(97)00666-X

F. Gerbier, A. Widera, S. Fölling, O. Mandel, and I. Bloch, Resonant control of spin dynamics in ultracold quantum gases by microwave dressing, Physical Review A, vol.72, issue.4, p.41602, 2006.
DOI : 10.1103/PhysRevLett.96.050402

URL : https://hal.archives-ouvertes.fr/hal-00116285

M. Chang, Q. Qin, W. Zhang, L. You, and M. S. Chapman, Coherent spinor dynamics in a spin-1 Bose??condensate, Nature Physics, vol.79, issue.2, p.111, 2005.
DOI : 10.1038/18395

M. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier et al., Bose-Einstein Condensates, Physical Review Letters, vol.69, issue.14, p.140403, 2004.
DOI : 10.1103/PhysRevA.60.1463

URL : https://hal.archives-ouvertes.fr/hal-01159883

A. T. Black, E. Gomez, L. D. Turner, S. Jung, and P. D. Lett, Spinor Dynamics in an Antiferromagnetic Spin-1 Condensate, Physical Review Letters, vol.99, issue.7, p.70403, 2007.
DOI : 10.1103/PhysRevLett.93.163602

L. Sadler, . Jm-higbie, . Leslie, D. Vengalattore, and . Stamper-kurn, Spontaneous symmetry breaking in a quenched ferromagnetic spinor bose?einstein condensate, Nature, issue.7109, pp.443312-315, 2006.
DOI : 10.1038/nature05094

A. Vinit, E. M. Bookjans, C. A. Sá-de-melo, and C. Raman, Antiferromagnetic Spatial Ordering in a Quenched One-Dimensional Spinor Gas, Physical Review Letters, vol.110, issue.16, p.110, 2013.
DOI : 10.1103/RevModPhys.49.435

D. Jacob, L. Shao, V. Corre, T. Zibold, L. D. Sarlo et al., Phase diagram of spin-1 antiferromagnetic Bose-Einstein condensates, Physical Review A, vol.86, issue.6, p.61601, 2012.
DOI : 10.1103/PhysRevA.70.043611

URL : https://hal.archives-ouvertes.fr/hal-00840678

J. Stenger, D. Inouye, H. Stamper-kurn, . Miesner, W. Chikkatur et al., Spin domains in ground-state bose-einstein condensates, Nature, issue.6709, pp.396345-348, 1998.

E. M. Bookjans, A. Vinit, and C. Raman, Quantum Phase Transition in an Antiferromagnetic Spinor Bose-Einstein Condensate, Physical Review Letters, vol.107, issue.19, 2011.
DOI : 10.1080/00018739400101505

URL : http://arxiv.org/abs/1109.1012

A. Vinit and C. Raman, Precise measurements on a quantum phase transition in antiferromagnetic spinor Bose-Einstein condensates, Physical Review A, vol.95, issue.1, 2017.
DOI : 10.1103/PhysRevA.82.031602

M. Vengalattore, S. R. Leslie, J. Guzman, and D. M. Stamper-kurn, Spontaneously Modulated Spin Textures in a Dipolar Spinor Bose-Einstein Condensate, Physical Review Letters, vol.100, issue.17, p.100, 2008.
DOI : 10.1103/PhysRevLett.95.050401

URL : http://arxiv.org/abs/0712.4182

M. Fattori, T. Koch, S. Goetz, A. Griesmaier, S. Hensler et al., Demagnetization cooling of a gas, Nature Physics, vol.15, issue.11, pp.765-768, 2006.
DOI : 10.1103/PhysRevLett.96.143005

B. Pasquiou, E. Maréchal, G. Bismut, P. Pedri, L. Vernac et al., Spontaneous demagnetization of a dipolar spinor bose gas in an ultralow magnetic ield, Physical Review Letters, issue.25, p.106, 2011.

B. Naylor, E. Maréchal, J. Huckans, O. Gorceix, P. Pedri et al., Cooling of a Bose-Einstein Condensate by Spin Distillation, Physical Review Letters, vol.115, issue.24, p.243002, 2015.
DOI : 10.1103/PhysRevA.66.031601

URL : https://hal.archives-ouvertes.fr/hal-01153675

J. Stuhler, A. Griesmaier, T. Koch, M. Fattori, T. Pfau et al., Observation of Dipole-Dipole Interaction in a Degenerate Quantum Gas, Physical Review Letters, vol.31, issue.15, p.95, 2005.
DOI : 10.1103/PhysRevLett.89.130401

URL : https://hal.archives-ouvertes.fr/hal-00012490

G. Bismut, B. Laburthe-tolra, E. Maréchal, P. Pedri, O. Gorceix et al., Anisotropic Excitation Spectrum of a Dipolar Quantum Bose Gas, Physical Review Letters, vol.109, issue.15
DOI : 10.1103/PhysRevLett.90.250403

URL : https://hal.archives-ouvertes.fr/hal-00703010

T. Isoshima, T. Ohmi, and K. Machida, Double Phase Transitions in Magnetized Spinor Bose-Einstein Condensation, Journal of the Physical Society of Japan, vol.69, issue.12, pp.3864-3869, 2000.
DOI : 10.1143/JPSJ.69.3864

URL : http://arxiv.org/abs/cond-mat/0005289

T. Ho, Spinor Bose Condensates in Optical Traps, Physical Review Letters, vol.18, issue.4, p.742, 1998.
DOI : 10.1103/PhysRevLett.81.742

URL : http://arxiv.org/abs/cond-mat/9803231

A. F. Andreev and I. A. Grishchuk, Spin nematics, Sov.Phys.-JETP 1984, pp.467-475, 1984.

M. Blume and Y. Y. Hsieh, Biquadratic Exchange and Quadrupolar Ordering, Journal of Applied Physics, vol.40, issue.3, pp.1249-1249, 1969.
DOI : 10.1088/0370-1328/86/1/128

P. G. De-gennes and J. Prost, he Physics of Liquid Crystals, 1995.

P. Chandra, P. Coleman, and I. Ritchey, Magnets without moments: Spin nematics and beyond (invited), Journal of Applied Physics, vol.61, issue.8, pp.694974-4978, 1991.
DOI : 10.1103/PhysRevLett.64.2070

P. Chandra and P. Coleman, Quantum spin nematics: Moment-free magnetism, Physical Review Letters, vol.52, issue.1, pp.100-103, 1991.
DOI : 10.1103/PhysRevLett.66.100

H. H. Chen and P. M. Levy, Quadrupole Phase Transitions in Magnetic Solids, Physical Review Letters, vol.26, issue.20, pp.1383-1385, 1971.
DOI : 10.1103/PhysRevLett.27.1383

S. Nakatsuji, Y. Nambu, H. Tonomura, O. Sakai, S. Jonas et al., Spin Disorder on a Triangular Lattice, Yiming Qiu, and Yoshiteru Maeno, pp.1697-1700, 2005.
DOI : 10.1126/science.1114727

H. Tsunetsugu and M. Arikawa, =1 Triangular Antiferromagnets, Journal of the Physical Society of Japan, vol.75, issue.8, p.83701, 2006.
DOI : 10.1143/JPSJ.75.083701

A. Läuchli, F. Mila, and K. Penc, Bilinear-Biquadratic Heisenberg Model on the Triangular Lattice, Physical Review Letters, vol.60, issue.8, p.87205, 2006.
DOI : 10.1007/s100510070242

F. Michaud, F. Vernay, and F. Mila, Theory of inelastic light scattering in spin-1 systems: Resonant regimes and detection of quadrupolar order, Physical Review B, vol.84, issue.18, p.184424, 2011.
DOI : 10.1016/0550-3213(88)90073-9

A. Imambekov, M. D. Lukin, and E. Demler, Spin-exchange interactions of spin-one bosons in optical lattices: Singlet, nematic, and dimerized phases, Physical Review A, vol.83, issue.6, p.63602, 2003.
DOI : 10.1103/PhysRevA.68.063602

M. Snoek and F. Zhou, Microscopic wave functions of spin-singlet and nematic Mott states of spin-one bosons in high-dimensional bipartite lattices, Physical Review B, vol.68, issue.9, p.94410, 2004.
DOI : 10.1103/PhysRevB.69.094410

F. Zhou, M. Snoek, J. Wiemer, and I. Aleck, Magnetically stabilized nematic order:???Three-dimensional bipartite optical lattices, Physical Review B, vol.43, issue.18, p.184434, 2004.
DOI : 10.1103/PhysRevA.69.033606

F. Zhou, Quantum Spin Nematic States in Bose???Einstein Condensates, International Journal of Modern Physics B, vol.63, issue.14, pp.2643-2698, 2003.
DOI : 10.1103/PhysRevLett.60.821

URL : http://arxiv.org/abs/cond-mat/0108473

H. Laurent-de-forges-de-parny, F. Yang, and . Mila, Anderson Tower of States and Nematic Order of Spin-1 Bosonic Atoms on a 2D Lattice, Physical Review Letters, vol.113, issue.20, 2014.
DOI : 10.1103/PhysRevB.81.184526

D. Podolsky and E. Demler, Properties and detection of spin nematic order in strongly correlated electron systems, New Journal of Physics, vol.7, issue.1, p.59, 2005.
DOI : 10.1088/1367-2630/7/1/059

M. Dan, M. Stamper-kurn, and . Ueda, Spinor Bose gases: Symmetries, magnetism, and quantum dynamics, Reviews of Modern Physics, vol.85, issue.3, pp.1191-1244, 2013.

T. Ohmi and T. Machida, Bose-Einstein Condensation with Internal Degrees of Freedom in Alkali Atom Gases, Journal of the Physical Society of Japan, vol.67, issue.6, p.1822, 1998.
DOI : 10.1143/JPSJ.67.1822

W. Huang, S. Gou, and Y. Tsai, Transition temperature for the all-optical formation of F=1 spinor condensate, Physical Review A, issue.6, p.65, 2002.

S. Uchino, M. Kobayashi, and M. Ueda, Bogoliubov theory and Lee-Huang-Yang corrections in spin-1 and spin-2 Bose-Einstein condensates in the presence of the quadratic Zeeman effect, Physical Review A, vol.11, issue.6, p.63632, 2010.
DOI : 10.1103/PhysRevA.77.033628

Y. Kao and T. F. Jiang, Transition temperatures of the trapped ideal spinor Bose gas, The European Physical Journal D, vol.34, issue.2, pp.263-269, 2006.
DOI : 10.1140/epjd/e2006-00157-4

K. Kis-szabó, P. Szépfalusy, and G. Szirmai, Phases of a polar spin-1 Bose gas in a magnetic field, Physics Letters A, vol.364, issue.5, pp.362-367, 2007.
DOI : 10.1016/j.physleta.2006.12.043

W. Zhang, S. Yi, and L. You, Bose-Einstein condensation of trapped interacting spin-1 atoms, Physical Review A, vol.109, issue.4, p.43611, 2004.
DOI : 10.1103/PhysRevA.68.031604

URL : http://arxiv.org/abs/cond-mat/0409680

Y. Nguyen-hanh-phuc, M. Kawaguchi, and . Ueda, Rb Bose-Einstein condensate, Physical Review A, vol.11, issue.4, p.43645, 2011.
DOI : 10.1103/PhysRev.104.576

Y. Kawaguchi, P. Nguyen-hanh-phuc, and . Blair-blakie, Finite-temperature phase diagram of a spin-1 Bose gas, Physical Review A, vol.85, issue.5, p.53611, 2012.
DOI : 10.1103/PhysRevLett.97.130404

G. Lang and E. Witkowska, Thermodynamics of a spin-1 Bose gas with fixed magnetization, Physical Review A, vol.90, issue.4, p.43609, 2014.
DOI : 10.1088/1367-2630/15/11/113039

L. Pitaevskii and S. Stringari, Bose-Einstein Condensation and Superluidity, 2016.

J. Christopher, H. Pethick, and . Smith, Bose-Einstein Condensation in Dilute Gases, 2008.

S. Grossmann and M. Holthaus, Abstract, Zeitschrift f??r Naturforschung A, vol.50, issue.10, 1995.
DOI : 10.1515/zna-1995-1003

S. Grossmann and M. Holthaus, On Bose-Einstein condensation in harmonic traps, Physics Letters A, vol.208, issue.3, pp.188-192, 1995.
DOI : 10.1016/0375-9601(95)00766-V

H. Haugerud, T. Haugset, and F. , A more accurate analysis of Bose-Einstein condensation in harmonic traps, Physics Letters A, vol.225, issue.1-3, pp.18-22, 1997.
DOI : 10.1016/S0375-9601(96)08842-1

W. Ketterle and N. J. Van-druten, Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions, Physical Review A, vol.97, issue.1, pp.656-660, 1996.
DOI : 10.1103/PhysRevA.54.656

T. Haugset, H. Haugerud, and J. O. Andersen, Bose-Einstein condensation in anisotropic harmonic traps, Physical Review A, vol.77, issue.4, pp.2922-2929, 1997.
DOI : 10.1103/PhysRevA.55.2922

URL : http://arxiv.org/abs/cond-mat/9611061

S. Giorgini, S. Pitaevskii, and . Stringari, Thermodynamics of a Trapped Bose-Condensed Gas, Journal of Low Temperature Physics, vol.54, issue.1-2, pp.309-355, 1997.
DOI : 10.1007/s10909-005-0089-x

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.257-261, 1999.
DOI : 10.1007/s003400050805

J. Dalibard, Collisional dynamics of ultra-cold atomic gases, Proceedings of the International School of Physics-Enrico Fermi, p.14, 1999.

S. Knoop, T. Schuster, R. Scelle, A. Trautmann, J. Appmeier et al., Feshbach spectroscopy and analysis of the interaction potentials of ultracold sodium, Physical Review A, vol.101, issue.4, p.42704, 2011.
DOI : 10.1103/PhysRevA.59.578

V. Victor, . Goldman, F. Isaac, . Silvera, J. Anthony et al., Atomic hydrogen in an inhomogeneous magnetic ield: Density proile and bose-einstein condensation, Physical Review B, vol.24, issue.5, p.2870, 1981.

A. David, . Huse, D. Eric, and . Siggia, he density distribution of a weakly interacting bose gas in an external potential, Journal of Low Temperature Physics, vol.46, issue.12, pp.137-149, 1982.

S. Giorgini, L. P. Pitaevskii, and S. Stringari, Condensate fraction and critical temperature of a trapped interacting Bose gas, Physical Review A, vol.53, issue.6, pp.4633-4636, 1996.
DOI : 10.1103/PhysRevA.54.R4633

F. Gerbier, Condensats de Bose-Einstein dans un piège anisotrope. heses, 2003.

L. Simon and W. T. Strunz, Bose gas in a single-beam optical dipole trap, Physical Review A, vol.81, issue.6, 2010.
DOI : 10.1103/PhysRevA.53.381

URL : http://arxiv.org/abs/0912.4513

W. Ketterle and N. Van-druten, Evaporative cooling of trapped atoms Advances in atomic, molecular, and optical physics, pp.181-236, 1996.

D. W. Snoke and J. P. Wolfe, Population dynamics of a Bose gas near saturation, Physical Review B, vol.23, issue.7, pp.4030-4037, 1989.
DOI : 10.1103/PhysRevB.39.4030

K. Helmerson, A. Martin, and D. E. Pritchard, Laser cooling of magnetically trapped neutral atoms, Journal of the Optical Society of America B, vol.9, issue.11, 1988.
DOI : 10.1364/JOSAB.9.001988

C. R. Monroe, E. A. Cornell, C. A. Sackett, C. J. Myatt, and C. E. Wieman, =30 ??K, Physical Review Letters, vol.46, issue.4, pp.414-417, 1993.
DOI : 10.1103/PhysRevLett.70.414

D. Suchet, M. Rabinovic, N. Homas-reimann, F. Kretschmar, C. Sievers et al., Analog simulation of Weyl particles with cold atoms, EPL (Europhysics Letters), vol.114, issue.2, p.26005, 2016.
DOI : 10.1209/0295-5075/114/26005

URL : https://hal.archives-ouvertes.fr/hal-01174057

W. Bao and Y. Cai, Mathematical theory and numerical methods for Bose-Einstein condensation, Kinetic and Related Models, vol.6, issue.1, pp.1-135, 2013.
DOI : 10.3934/krm.2013.6.1

URL : http://arxiv.org/abs/1212.5341

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, issue.5221, pp.269198-201, 1995.

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

V. Corre, Magnetism in spin-1 Bose-Einstein condensates with antiferromagnetic interactions, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01117109

M. Ueda and Y. Kawaguchi, Spinor Bose???Einstein Condensate, 2000.
DOI : 10.1142/9789812839602_0006

G. Bismut, B. Pasquiou, E. Maréchal, P. Pedri, L. Vernac et al., Collective Excitations of a Dipolar Bose-Einstein Condensate, Physical Review Letters, vol.105, issue.4, 2010.
DOI : 10.1103/PhysRevLett.77.5315

URL : https://hal.archives-ouvertes.fr/hal-00484061

T. Lahaye, J. Metz, B. Fröhlich, T. Koch, M. Meister et al., -Wave Collapse and Explosion of a Dipolar Bose-Einstein Condensate, Physical Review Letters, vol.72, issue.8, 2008.
DOI : 10.1103/PhysRevA.64.031601

URL : https://hal.archives-ouvertes.fr/hal-00600301

K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler et al., Bose-Einstein Condensation of Erbium, Physical Review Letters, vol.108, issue.21, 2012.
DOI : 10.1038/nature08953

URL : http://arxiv.org/abs/1204.1725

J. Christopher and . Foot, Atomic physics, 2005.

D. A. Steck, Sodium d line data, 2003.

G. Breit and I. I. Rabi, Measurement of Nuclear Spin, Physical Review, vol.38, issue.11, pp.2082-2083, 1931.
DOI : 10.1103/PhysRev.38.2082.2

S. Yi, Ö. E. Müstecapl?o?lu, C. P. Sun, and L. You, Single-mode approximation in a spinor-1 atomic condensate, Physical Review A, vol.6, issue.1, p.11601, 2002.
DOI : 10.1103/PhysRevA.66.011601

URL : http://arxiv.org/abs/cond-mat/0201173

T. Isoshima, K. Machida, and T. Ohmi, Spin-domain formation in spinor Bose-Einstein condensation, Physical Review A, vol.58, issue.6, pp.4857-4863, 1999.
DOI : 10.1103/PhysRevA.60.4857

URL : http://arxiv.org/abs/cond-mat/9905182

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates, Physical Review Letters, issue.8, pp.811539-1542, 1998.
DOI : 10.1142/9789812813787_0071

H. Pu, C. K. Law, and N. P. Bigelow, Complex quantum gases: spinor Bose???Einstein condensates of trapped atomic vapors, Physica B: Condensed Matter, vol.280, issue.1-4, pp.1-427, 2000.
DOI : 10.1016/S0921-4526(99)01429-5

W. Zhang, S. Yi, and L. You, Bose-Einstein condensation of trapped interacting spin-1 atoms, Physical Review A, vol.109, issue.4, p.43611, 2004.
DOI : 10.1103/PhysRevA.68.031604

URL : http://arxiv.org/abs/cond-mat/0409680

G. Lang and E. Witkowska, Thermodynamics of a spin-1 Bose gas with fixed magnetization, Physical Review A, vol.90, issue.4, p.43609, 2014.
DOI : 10.1088/1367-2630/15/11/113039

W. Ketterle, D. S. Durfee, and D. M. Stamper-kurn, Making, probing and understanding bose-einstein condensates, Proceedings of the International School on Physics Enrico Fermi Bose-Einstein Condensation in Atomic Gases, pp.67-176, 1998.

E. Mimoun, Condensat de Bose-Einstein de sodium dans un piège mésoscopique, 2010.

D. Jacob, Condensats de Bose-Einstein de spin 1: étude expérimentale avec des atomes de sodium dans un piège optique, 2012.

L. Shao, heoretical and experimental study of spin-1 antiferromagnetic Bose-Einstein Condensates. heses, Ecole Normale Supérieure, 2014.

J. Harold, P. Metcalf, and . Straten, Laser cooling and trapping of neutral atoms, 2007.

J. Dalibard, Une brève histoire des atomes froids, Cours du Collège de France, 2015.

J. Dalibard, Atomes ultra-froids

E. Mimoun, L. D. Sarlo, D. Jacob, J. Dalibard, and F. Gerbier, Fast production of ultracold sodium gases using light-induced desorption and optical trapping, Physical Review A, vol.27, issue.2, p.23631, 2010.
DOI : 10.1103/PhysRevA.80.053420

URL : https://hal.archives-ouvertes.fr/hal-00436570

A. Keshet and W. Ketterle, A distributed, graphical user interface based, computer control system for atomic physics experiments, Review of Scientific Instruments, vol.84, issue.1, p.15105, 2013.
DOI : 10.1063/1.1642741

V. Dugrain, P. Rosenbusch, and J. Reichel, Alkali vapor pressure modulation on the 100??ms scale in a single-cell vacuum system for cold atom experiments, Review of Scientific Instruments, vol.85, issue.8, p.83112, 2014.
DOI : 10.1364/OL.17.000526

E. Mimoun, L. Sarlo, J. Zondy, J. Dalibard, and F. Gerbier, Solid-state laser system for laser cooling of sodium, Applied Physics B, vol.16, issue.1-2, pp.31-40, 2010.
DOI : 10.1007/s00340-009-3844-x

URL : https://hal.archives-ouvertes.fr/hal-00467275

P. Juncar, . Pinard, A. Hamon, and . Chartier, Lines by Using a CW Tunable Dye Laser Stabilized on Iodine, Metrologia, vol.17, issue.3, p.77, 1981.
DOI : 10.1088/0026-1394/17/3/001

J. H. Shirley, Modulation transfer processes in optical heterodyne saturation spectroscopy, Optics Letters, vol.7, issue.11, p.537, 1982.
DOI : 10.1364/OL.7.000537

J. Zhang, D. Wei, C. Xie, and K. Peng, Characteristics of absorption and dispersion for rubidium D2 lines with the modulation transfer spectrum, Optics Express, vol.11, issue.11, pp.1338-1344, 2003.
DOI : 10.1364/OE.11.001338

D. Mccarron, S. King, and S. Cornish, Modulation transfer spectroscopy in atomic rubidium, Measurement Science and Technology, vol.19, issue.10, p.105601, 2008.
DOI : 10.1088/0957-0233/19/10/105601

R. Le-targat, J. Zondy, and P. Lemonde, 75%-Efficiency blue generation from an intracavity PPKTP frequency doubler, Optics Communications, vol.247, issue.4-6, pp.471-481, 2005.
DOI : 10.1016/j.optcom.2004.11.081

URL : https://hal.archives-ouvertes.fr/hal-00002488

D. Jacob, . Mimoun, . De-sarlo, . Weitz, F. Dalibard et al., Production of sodium Bose???Einstein condensates in an optical dimple trap, New Journal of Physics, vol.13, issue.6, p.65022, 2011.
DOI : 10.1088/1367-2630/13/6/065022

URL : https://hal.archives-ouvertes.fr/hal-00583436

M. Scholl, Probing an ytterbium Bose-Einstein condensate using an ultranarrow optical line : towards artiicial gauge ields in optical lattices. heses, 2014.

T. Kinoshita, T. Wenger, and D. S. Weiss, All-optical Bose-Einstein condensation using a compressible crossed dipole trap, Physical Review A, vol.269, issue.1, 2005.
DOI : 10.1103/PhysRevLett.85.2228

C. Hung, X. Zhang, N. Gemelke, and C. Chin, Accelerating evaporative cooling of atoms into Bose-Einstein condensation in optical traps, Physical Review A, vol.37, issue.1, 2008.
DOI : 10.1103/PhysRevA.57.4747

J. Clément, J. Brantut, M. Robert-de-saint-vincent, R. A. Nyman, A. Aspect et al., All-optical runaway evaporation to Bose-Einstein condensation, Physical Review A, vol.11, issue.6, p.79, 2009.
DOI : 10.1007/s00340-006-2363-2

D. M. Stamper-kurn, H. Miesner, A. P. Chikkatur, S. Inouye, J. Stenger et al., Reversible Formation of a Bose-Einstein Condensate, Physical Review Letters, vol.75, issue.11, pp.812194-2197, 1998.
DOI : 10.1103/PhysRevLett.81.2194

T. Weber, Bose-Einstein Condensation of Cesium, Science, vol.299, issue.5604, pp.232-235, 2002.
DOI : 10.1126/science.1079699

Z. Ma, C. Homas, S. Foot, and . Cornish, he evaporative cooling of a gas of caesium atoms in the hydrodynamic regime, Journal of Physics B: Atomic, Molecular and Optical Physics, issue.16, pp.363533-3540, 2003.

. Zhao-yuan, . Ma, J. Christopher, . Foot, L. Simon et al., Optimized evaporative cooling using a dimple potential: an eicient route to bose?einstein condensation, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.37, issue.15, pp.3187-3195, 2004.

D. Comparat, A. Fioretti, G. Stern, E. Dimova, B. L. Tolra et al., Optimized production of large Bose-Einstein condensates, Physical Review A, vol.33, issue.4, 2006.
DOI : 10.1103/PhysRevA.72.033408

URL : https://hal.archives-ouvertes.fr/hal-00018383

D. B. Hume, I. Stroescu, M. Joos, W. Muessel, H. Strobel et al., Accurate Atom Counting in Mesoscopic Ensembles, Physical Review Letters, vol.111, issue.25, p.111, 2013.
DOI : 10.1038/nature09378

URL : http://arxiv.org/abs/1307.7598

G. Reinaudi, . Lahaye, D. Wang, and . Guéry-odelin, Strong saturation absorption imaging of dense clouds of ultracold atoms, Optics Letters, vol.32, issue.21, pp.3143-3145, 2007.
DOI : 10.1364/OL.32.003143

L. Chomaz, . Corman, . Yefsah, J. Desbuquois, and . Dalibard, Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis, New Journal of Physics, vol.14, issue.5, p.55001, 2012.
DOI : 10.1088/1367-2630/14/5/055001

S. D. Jenkins, J. Ruostekoski, J. Javanainen, R. Bourgain, S. Jennewein et al., Optical resonance shits in the luorescence of thermal and cold atomic gases, Physical Review Letters, issue.18, p.116, 2016.

T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, and J. Dalibard, Exploring the Thermodynamics of a Two-Dimensional Bose Gas, Physical Review Letters, vol.34, issue.13, p.2011
DOI : 10.1103/PhysRevLett.106.105301

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

S. Friebel, C. D-'andrea, J. Walz, M. Weitz, and T. W. Hänsch, -laser optical lattice with cold rubidium atoms, Physical Review A, vol.75, issue.1, pp.20-23, 1998.
DOI : 10.1103/PhysRevA.57.R20

URL : https://hal.archives-ouvertes.fr/hal-00534539

S. Balik, A. L. Win, and M. D. Havey, Imaging-based parametric resonance in an optical dipole-atom trap, Physical Review A, vol.42, issue.2, 2009.
DOI : 10.1103/PhysRevA.64.033403

URL : http://arxiv.org/abs/0908.0263

V. Makhalov, K. Martiyanov, T. Barmashova, and A. Turlapov, Precision measurement of a trapping potential for an ultracold gas, Physics Letters A, vol.379, issue.4, pp.327-332, 2015.
DOI : 10.1016/j.physleta.2014.10.049

W. Kohn, Cyclotron Resonance and de Haas-van Alphen Oscillations of an Interacting Electron Gas, Physical Review, vol.121, issue.4, pp.1242-1244, 1961.
DOI : 10.1103/PhysRev.123.1242

J. F. Dobson, Harmonic-Potential Theorem: Implications for Approximate Many-Body Theories, Physical Review Letters, vol.49, issue.16, pp.2244-2247, 1994.
DOI : 10.1103/PhysRevLett.73.2244

W. Gerlach and O. Stern, Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld, Zeitschrift f???r Physik, vol.9, issue.1, pp.349-352, 1922.
DOI : 10.1007/BF01326983

W. Gerlach and O. Stern, ??ber die Richtungsquantelung im Magnetfeld, Annalen der Physik, vol.3, issue.16, pp.673-699, 1924.
DOI : 10.1002/andp.19243791602

T. E. Phipps and J. B. Taylor, The Magnetic Moment of the Hydrogen Atom, Physical Review, vol.116, issue.2, pp.309-320, 1927.
DOI : 10.1103/PhysRev.29.309

W. Joseph and . Goodman, Speckle phenomena in optics: theory and applications, 2007.

W. Joseph and . Goodman, Some fundamental properties of speckle, JOSA, vol.66, issue.11, pp.1145-1150, 1976.

J. Hector, R. Rabal, and . Jr, Dynamic laser speckle and applications, 2008.

S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber et al., Noise in laser speckle correlation and imaging techniques, Optics Express, vol.18, issue.14, p.14519, 2010.
DOI : 10.1364/OE.18.014519

URL : https://hal.archives-ouvertes.fr/hal-00495388

J. Lewis, Fast normalized cross-correlation, Vision interface, pp.120-123, 1995.

X. Li, M. Ke, B. Yan, and Y. Wang, Reduction of interference fringes in absorption imaging of cold atom cloud using eigenface method, Chin. Opt. Lett, vol.5, issue.3, pp.128-130, 2007.

C. Ockeloen, . Tauschinsky, S. Spreeuw, and . Whitlock, Detection of small atom numbers through image processing, Physical Review A, vol.5, issue.6, p.61606, 2010.
DOI : 10.1088/0953-4075/43/15/155002

URL : https://pure.uva.nl/ws/files/1027017/89008_330117.pdf

C. F. Ockeloen, Probing luctuations in a lattice of mesoscopic atomic ensembles. Master's thesis, van der Waals-Zeeman Institute, 2010.

P. L. Gould, G. A. Ruf, and D. E. Pritchard, Difraction of atoms by light: he near-resonant kapitza-dirac efect, Physical Review Letters, issue.8, pp.56827-830, 1986.
DOI : 10.1103/physrevlett.56.827

P. Jefery-ungar, S. David, E. Weiss, S. Riis, and . Chu, Optical molasses and multilevel atoms: theory, Journal of the Optical Society of America B, vol.6, issue.11, pp.2058-2071, 1989.
DOI : 10.1364/JOSAB.6.002058

I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, A New Method of Measuring Nuclear Magnetic Moment, Physical Review, vol.9, issue.4, pp.318-318, 1938.
DOI : 10.1103/PhysRev.53.318

A. Michael, . Lombardi, . Heavner, R. Steven, and . Jeferts, Nist primary frequency standards and the realization of the si second, NCSLI Measure, vol.2, issue.4, pp.74-89, 2007.

C. P. Slichter, Principles of Magnetic Resonance, 1990.

C. Cohen-tannoudji, J. Dupont-roc, and G. Grynberg, Processus d'interaction entre photons et atomes, 2012.

R. Loudon, he quantum theory of light, OUP Oxford, 2000.

M. Lombardi, Cr??ation d'orientation par combinaison de deux alignements alignement et orientation des niveaux excit??s d'une d??charge haute fr??quence, Journal de Physique, vol.30, issue.8-9, pp.8-9631, 1969.
DOI : 10.1051/jphys:01969003008-9063100

C. Cohen-tannoudji and J. Dupont-roc, Orientation, par action d'un champ electrique ???fictif???, d'une vapeur initialement alignee, Optics Communications, vol.1, issue.4, pp.184-186, 1969.
DOI : 10.1016/0030-4018(69)90061-3

F. Bloch, Nuclear Induction, Physical Review, vol.56, issue.7-8, pp.460-474, 1946.
DOI : 10.1103/PhysRev.70.460

K. Jiménez-garcía, Artiicial Gauge Fields for Ultracold Neutral Atoms, 2012.

T. Zibold, V. Corre, C. Frapolli, A. Invernizzi, J. Dalibard et al., Spin-nematic order in antiferromagnetic spinor condensates, Physical Review A, vol.60, issue.2, p.93, 2016.
DOI : 10.1103/RevModPhys.71.463

URL : https://hal.archives-ouvertes.fr/hal-01280752

V. Corre, C. Zibold, . Frapolli, . Shao, F. Dalibard et al., Spin-1 condensates at thermal equilibrium: A SU(3) coherent state approach, EPL (Europhysics Letters), vol.110, issue.2, p.26001, 2015.
DOI : 10.1209/0295-5075/110/26001

URL : http://arxiv.org/abs/1502.06024

Y. Kawaguchi and M. Ueda, Spinor Bose???Einstein condensates, Physics Reports, vol.520, issue.5, pp.253-381, 2012.
DOI : 10.1016/j.physrep.2012.07.005

URL : http://arxiv.org/abs/1001.2072

C. J. Mullin, J. M. Keller, C. L. Hammer, and R. H. Good, Polarization and alignment of spin one states, Annals of Physics, vol.37, issue.1, pp.55-61, 1966.
DOI : 10.1016/0003-4916(66)90276-4

B. A. Ivanov and A. K. Kolezhuk, quantum nematic, Physical Review B, vol.64, issue.144, p.52401, 2003.
DOI : 10.1103/PhysRevB.68.052401

K. Murata, H. Saito, and M. Ueda, Broken-axisymmetry phase of a spin-1 ferromagnetic Bose-Einstein condensate, Physical Review A, vol.11, issue.1, 2007.
DOI : 10.1103/PhysRevLett.96.065302

B. Lücke, M. Scherer, J. Kruse, L. Pezzé, F. Deuretzbacher-peise et al., Twin Matter Waves for Interferometry Beyond the Classical Limit, Science, vol.100, issue.8, pp.334773-776, 2011.
DOI : 10.1103/PhysRevLett.100.080405

C. Gross, . Strobel, . Nicklas, N. Zibold, . Bar-gill et al., Atomic homodyne detection of continuous-variable entangled twin-atom states, Nature, vol.7, issue.7376, pp.480-219, 2011.
DOI : 10.1038/nature10654

URL : http://arxiv.org/abs/1112.4594

B. Lücke, J. Peise, G. Vitagliano-arlt, L. Santos, G. Tóth et al., Detecting Multiparticle Entanglement of Dicke States, Physical Review Letters, vol.112, issue.15, p.155304, 2014.
DOI : 10.1142/S0219749913300015

M. Naraschewski and D. M. Stamper-kurn, Analytical description of a trapped semi-ideal Bose gas at finite temperature, Physical Review A, vol.9, issue.3, pp.2423-2426, 1998.
DOI : 10.1103/PhysRevA.58.2423

B. Pasquiou, E. Maréchal, L. Vernac, O. Gorceix, and B. , Thermodynamics of a Bose-Einstein Condensate with Free Magnetization, Physical Review Letters, vol.108, issue.4, p.45307, 2012.
DOI : 10.1103/PhysRevLett.106.195301

URL : https://hal.archives-ouvertes.fr/hal-00629239

B. Naylor, M. Brewczyk, M. Gajda, O. Gorceix, E. Maréchal et al., Competition between Bose-Einstein Condensation and Spin Dynamics, Physical Review Letters, vol.117, issue.18, p.117, 2016.
DOI : 10.1103/PhysRevA.84.063625

URL : https://hal.archives-ouvertes.fr/hal-01347485

R. Olf, F. Fang, G. E. Marti, A. Macrae, and D. M. Stamper-kurn, Thermometry and cooling of a Bose gas to 0.02 times the condensation temperature, Nature Physics, vol.19, issue.9, pp.720-723, 2015.
DOI : 10.1038/nphys3408

F. Fang, R. Olf, S. Wu, H. Kadau, and D. M. Stamper-kurn, Condensing Magnons in a Degenerate Ferromagnetic Spinor Bose Gas, Physical Review Letters, vol.116, issue.9, p.95301, 2016.
DOI : 10.1103/PhysRevLett.95.050401

URL : http://arxiv.org/abs/1511.05193

G. Bohm and G. Zech, Introduction to statistics and data analysis for physicists. DESY, 2010.

M. Holzmann, La transition de Bose-Einstein dans un gaz dilué. heses, 2000.

M. Holzmann, W. Krauth, and M. Naraschewski, Precision Monte Carlo test of the Hartree-Fock approximation for a trapped Bose gas, Physical Review A, vol.77, issue.4, pp.2956-2961, 1999.
DOI : 10.1103/PhysRevA.59.2956

M. Holzmann, P. Grüter, and F. Laloë, Bose-Einstein condensation in interacting gases, The European Physical Journal B, vol.10, issue.4, pp.739-760, 1999.
DOI : 10.1007/s100510050905

URL : https://hal.archives-ouvertes.fr/hal-00001409

J. R. Ensher, D. S. Jin, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Bose-einstein condensation in a dilute gas: Measurement of energy and ground-state occupation, Physical Review Letters, issue.25, pp.774984-4987, 1996.

R. P. Smith, R. L. Campbell, N. Tammuz, and Z. Hadzibabic, Efects of interactions on the critical temperature of a trapped bose gas, Physical Review Letters, vol.106, issue.25, 2011.

N. Tammuz, R. P. Smith, R. L. Campbell, and S. Beattie, Can a Bose Gas Be Saturated?, Physical Review Letters, vol.106, issue.23, 2011.
DOI : 10.1038/nphys1507

URL : http://arxiv.org/abs/1103.2896

A. Imambekov, E. Demler, and M. D. Lukin, Magnetization Plateaus for Spin-One Bosons in Optical Lattices: Stern-Gerlach Experiments with Strongly Correlated Atoms, Physical Review Letters, vol.251, issue.12, p.120405, 2004.
DOI : 10.1103/PhysRevA.69.031601

P. A. Matthew, P. B. Fisher, G. Weichman, D. S. Grinstein, and . Fisher, Boson localization and the superluid-insulator transition, Physical Review B, vol.40, issue.1, pp.546-570, 1989.

A. Sala, D. L. Núñez, J. Martorell, L. D. Sarlo, T. Zibold et al., Artur Polls, and Bruno Juliá-Díaz. Shortcut to adiabaticity in spinor condensates, Physical Review A, vol.94, issue.4, 2016.

T. ?wis?ocki, E. Witkowska, and M. Matuszewski, Nonadiabatic quantum phase transition in a trapped spinor condensate, Physical Review A, vol.24, issue.4
DOI : 10.1103/PhysRevLett.83.661

R. W. Boyd, Nonlinear Optics, 2003.

D. John, H. Bierlein, and . Vanherzeele, Potassium titanyl phosphate: properties and new applications, J. Opt. Soc. Am. B, vol.6, issue.4, pp.622-633, 1989.

K. Kato and E. Takaoka, Sellmeier and thermo-optic dispersion formulas for KTP, Applied Optics, vol.41, issue.24, pp.5040-5044, 2002.
DOI : 10.1364/AO.41.005040

G. Boyd and D. Kleinman, Parametric Interaction of Focused Gaussian Light Beams, Journal of Applied Physics, vol.265, issue.8, p.3597, 1968.
DOI : 10.1145/320954.320958

J. Hall, . Hollberg, H. Baer, and . Robinson, Optical heterodyne saturation spectroscopy, Applied Physics Letters, vol.44, issue.9, pp.680-682, 1981.
DOI : 10.1007/BF00900531

N. Goldman, . Juzeli¯-unas, I. Öhberg, and . Spielman, Light-induced gauge fields for ultracold atoms, Reports on Progress in Physics, vol.77, issue.12, p.126401, 2014.
DOI : 10.1088/0034-4885/77/12/126401

URL : http://arxiv.org/abs/1308.6533

A. R. Edmonds, Angular Momentum in Quantum Mechanics, 1996.

Y. Lin, K. Jimenez-garcia, and I. Spielman, Spin???orbit-coupled Bose???Einstein condensates, Nature, vol.79, issue.7336, pp.47183-86, 2011.
DOI : 10.1038/nature09887