I. Lesanovsky and W. V. 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

J. Fortágh and C. Zimmermann, Magnetic microtraps for ultracold atoms, Reviews of Modern Physics, vol.79, issue.1, p.235, 2007.
DOI : 10.1103/RevModPhys.79.235

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Reviews of Modern Physics, vol.82, issue.2, p.1225, 2010.
DOI : 10.1103/RevModPhys.82.1225

I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Reviews of Modern Physics, vol.80, issue.3, p.885, 2008.
DOI : 10.1103/RevModPhys.80.885

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

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas et al., Quantum Noise Limited and Entanglement-Assisted Magnetometry, Physical Review Letters, vol.104, issue.13, p.133601, 2010.
DOI : 10.1103/PhysRevLett.104.133601

J. Appel, P. J. Windpassinger, D. Oblak, U. B. Hoff, N. Kjaergaard et al., Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit, Proceedings of the National Academy of Sciences, vol.106, issue.27, p.10960, 2009.
DOI : 10.1073/pnas.0901550106

M. H. Schleier-smith, I. D. Leroux, and V. Vuletic, States of an Ensemble of Two-Level Atoms with Reduced Quantum Uncertainty, Physical Review Letters, vol.104, issue.7, p.73604, 2010.
DOI : 10.1103/PhysRevLett.104.073604

C. Gross, T. Zibold, E. Nicklas, J. Estève, and M. K. Oberthaler, Nonlinear atom interferometer surpasses classical precision limit, Nature, vol.32, issue.7292, p.1165, 2010.
DOI : 10.1038/nature08919

URL : http://arxiv.org/abs/1009.2374

M. F. Riedel, P. Bohi, Y. Li, T. W. Hansch, A. Sinatra et al., Atom-chip-based generation of entanglement for quantum metrology, Nature, vol.65, issue.7292, p.1170, 2010.
DOI : 10.1038/nature08988

M. Kitagawa and M. Ueda, Squeezed spin states, Physical Review A, vol.47, issue.6, p.5138, 1993.
DOI : 10.1103/PhysRevA.47.5138

A. Sørensen, L. Duan, J. I. Cirac, and P. Zoller, Many-particle entanglement with Bose- Einstein condensates, Nature, vol.409, issue.6816, p.63, 2001.
DOI : 10.1038/35051038

J. Estève, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, Squeezing and entanglement in a Bose???Einstein condensate, Nature, vol.96, issue.7217, p.1216, 2008.
DOI : 10.1038/nature07332

D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen, Squeezed atomic states and projection noise in spectroscopy, Physical Review A, vol.50, issue.1, p.67, 1994.
DOI : 10.1103/PhysRevA.50.67

V. Giovannetti, S. Lloyd, L. Maccone, and Q. Metrology, Quantum Metrology, Physical Review Letters, vol.96, issue.1, p.10401, 2006.
DOI : 10.1103/PhysRevLett.96.010401

L. Pezzé and A. Smerzi, Entanglement, Nonlinear Dynamics, and the Heisenberg Limit, Entanglement, Nonlinear Dynamics, and the Heisenberg Limit, p.100401, 2009.
DOI : 10.1103/PhysRevLett.102.100401

W. Dür and H. Briegel, Stability of Macroscopic Entanglement under Decoherence, Physical Review Letters, vol.92, issue.18, p.180403, 2004.
DOI : 10.1103/PhysRevLett.92.180403

F. Fröwis and W. Dür, Stable Macroscopic Quantum Superpositions, Physical Review Letters, vol.106, issue.11, p.110402, 2011.
DOI : 10.1103/PhysRevLett.106.110402

A. P. Hines, R. Mckenzie, and G. J. Milburn, Entanglement of two-mode Bose-Einstein condensates, Physical Review A, vol.67, issue.1, p.13609, 2003.
DOI : 10.1103/PhysRevA.67.013609

T. Hwang, C. Hwang, and C. Li, Multiparty quantum secret sharing based on GHZ states, Physica Scripta, vol.83, issue.4, p.45004, 2011.
DOI : 10.1088/0031-8949/83/04/045004

A. Sinatra and Y. Castin, Phase dynamics of Bose-Einstein condensates: Losses versus revivals, The European Physical Journal D - Atomic, Molecular and Optical Physics, vol.4, issue.3, p.247, 1998.
DOI : 10.1007/s100530050206

Y. Lin, P. Treutlein, J. Reichel, and A. Sinatra, Spin squeezing in a bimodal condensate: spatial dynamics and particle losses, Eur. Phys. J. D, vol.68, p.365, 2008.

G. Ferrini, D. Spehner, A. Minguzzi, and F. W. Hekking, Noise in Bose Josephson junctions: Decoherence and phase relaxation, Noise in Bose Josephson junctions: Decoherence and phase relaxation, p.33621, 2010.
DOI : 10.1103/PhysRevA.82.033621

URL : https://hal.archives-ouvertes.fr/hal-01060047

G. Ferrini, D. Spehner, A. Minguzzi, and F. W. Hekking, Effect of phase noise on quantum correlations in Bose-Josephson junctions, Effect of phase noise on quantum correlations in Bose Josephson junctions, p.43628, 2011.
DOI : 10.1103/PhysRevA.84.043628

URL : https://hal.archives-ouvertes.fr/hal-01060033

J. Anglin, Cold, Dilute, Trapped Bosons as an Open Quantum System, Physical Review Letters, vol.79, issue.1, 1997.
DOI : 10.1103/PhysRevLett.79.6

D. Witthaut, F. Trimborn, and S. Wimberger, Dissipation-induced coherence and stochastic resonance of an open two-mode Bose-Einstein condensate, Physical Review A, vol.79, issue.3, p.33621, 2009.
DOI : 10.1103/PhysRevA.79.033621

Y. P. Huang and M. G. Moore, Creation, detection, and decoherence of macroscopic quantum superposition states in double-well Bose-Einstein condensates, Physical Review A, vol.73, issue.2, p.23606, 2006.
DOI : 10.1103/PhysRevA.73.023606

M. G. Benedict and A. Czirjàk, Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms, Physical Review A, vol.60, issue.5, p.4034, 1999.
DOI : 10.1103/PhysRevA.60.4034

Y. Khodorkovsky, G. Kurizki, and A. Vardi, Decoherence and entanglement in a bosonic Josephson junction: Bose-enhanced quantum Zeno control of phase diffusion, Physical Review A, vol.80, issue.2, p.23609, 2009.
DOI : 10.1103/PhysRevA.80.023609

G. Ferrini, A. Minguzzi, and F. W. Hekking, Number squeezing, quantum fluctuations, and oscillations in mesoscopic Bose Josephson junctions, Physical Review A, vol.78, issue.2, p.23606, 2008.
DOI : 10.1103/PhysRevA.78.023606

URL : https://hal.archives-ouvertes.fr/hal-00377889

G. Ferrini, A. Minguzzi, and F. W. Hekking, Detection of coherent superpositions of phase states by full counting statistics in a Bose Josephson junction, Physical Review A, vol.80, issue.4, p.43628, 2009.
DOI : 10.1103/PhysRevA.80.043628

M. Lapert, G. Ferrini, and D. Sugny, Optimal control of quantum superpositions in a bosonic Josephson junction, Physical Review A, vol.85, issue.2, 2011.
DOI : 10.1103/PhysRevA.85.023611

URL : https://hal.archives-ouvertes.fr/hal-00760308

B. D. Josephson, Possible new effects in superconductive tunnelling, Physics Letters, vol.1, issue.7, p.251, 1962.
DOI : 10.1016/0031-9163(62)91369-0

L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation, 2003.

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. Davis, M. O. Mewes, M. Andrews, N. Van-druten, N. Durfee et al., Bose-Einstein Condensation in a Gas of Sodium Atoms, Phys. Rev. Lett, vol.75, p.1687, 1995.

C. J. Pethick and H. Smith, Bose-Einstein condensation in atomic gases, 2002.

J. Fortágh and C. Zimmermann, Magnetic microtraps for ultracold atoms, Reviews of Modern Physics, vol.79, issue.1, p.235, 2007.
DOI : 10.1103/RevModPhys.79.235

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

P. Bohi, M. F. Riedel, J. Hoffrogge, J. Reichel, T. W. Hänsch et al., Coherent manipulation of Bose???Einstein condensates with state-dependent microwave potentials on an atom chip, Nature Physics, vol.98, issue.8, p.592, 2009.
DOI : 10.1109/TMTT.1987.1133637

G. Jo, Y. Shin, S. Will, T. A. Pasquini, M. Saba et al., Long Phase Coherence Time and Number Squeezing of Two Bose-Einstein Condensates on an Atom Chip, Physical Review Letters, vol.98, issue.3, p.30407, 2007.
DOI : 10.1103/PhysRevLett.98.030407

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

C. A. Regal, M. Greiner, and D. S. Jin, Observation of Resonance Condensation of Fermionic Atom Pairs, Physical Review Letters, vol.92, issue.4, p.40403, 2004.
DOI : 10.1103/PhysRevLett.92.040403

L. V. Hau, B. D. Bush, C. Liu, Z. Dutton, M. M. Burns et al., Nearresonant spatial images of confined Bose-Einstein condensates in a 4-Dee magnetic bottle, Phys. Rev. A, vol.58, p.54, 1998.

W. Zhang and L. Duan, Tomography of correlation functions for ultracold atoms via time-of-flight images, Physical Review A, vol.80, issue.6, p.63614, 2009.
DOI : 10.1103/PhysRevA.80.063614

J. Javanainen, Oscillatory exchange of atoms between traps containing Bose condensates, Physical Review Letters, vol.57, issue.25, p.3164, 1986.
DOI : 10.1103/PhysRevLett.57.3164

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates, Physical Review Letters, vol.79, issue.25, p.4951, 1997.
DOI : 10.1103/PhysRevLett.79.4950

URL : http://arxiv.org/abs/cond-mat/9706221

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, oscillations, and macroscopic quantum self-trapping, Physical Review A, vol.59, issue.1, p.620, 1999.
DOI : 10.1103/PhysRevA.59.620

S. Giovanazzi, A. Smerzi, and S. Fantoni, Josephson Effects in Dilute Bose-Einstein Condensates, Physical Review Letters, vol.84, issue.20, p.4521, 2000.
DOI : 10.1103/PhysRevLett.84.4521

S. Levy, E. Lahoud, I. Shomroni, and J. Steinhauer, The a.c. and d.c. Josephson effects in a Bose???Einstein condensate, Nature, vol.273, issue.7162, p.6186, 2007.
DOI : 10.1038/nature06186

URL : https://hal.archives-ouvertes.fr/inria-00074279

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

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, Phys. Rev. Lett, vol.1539, p.81, 1998.

L. Pitaeskii and S. Stringari, Interference of Bose-Einstein Condensates in Momentum Space, Physical Review Letters, vol.83, issue.21, p.4237, 1999.
DOI : 10.1103/PhysRevLett.83.4237

L. Pitaeskii and S. Stringari, Thermal vs Quantum Decoherence in Double Well Trapped Bose-Einstein Condensates, Physical Review Letters, vol.87, issue.18, p.180402, 2001.
DOI : 10.1103/PhysRevLett.87.180402

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

R. Gati and M. K. Oberthaler, A bosonic Josephson junction, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.40, issue.10, p.61, 2007.
DOI : 10.1088/0953-4075/40/10/R01

P. Carruthers and M. M. Nieto, Coherent States and the Number-Phase Uncertainty Relation, Physical Review Letters, vol.14, issue.11, p.387, 1965.
DOI : 10.1103/PhysRevLett.14.387

R. Lynch, The quantum phase problem: a critical review, Physics Reports, vol.256, issue.6, p.367, 1995.
DOI : 10.1016/0370-1573(94)00095-K

T. Zibold, E. Nicklas, C. Gross, and M. K. Oberthaler, Classical Bifurcation at the Transition from Rabi to Josephson Dynamics, Physical Review Letters, vol.105, issue.20, p.204101, 2010.
DOI : 10.1103/PhysRevLett.105.204101

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential, Physical Review A, vol.55, issue.6, p.4318, 1997.
DOI : 10.1103/PhysRevA.55.4318

K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Exact Quantum Dynamics of a Bosonic Josephson Junction, Physical Review Letters, vol.103, issue.22, p.220601, 2009.
DOI : 10.1103/PhysRevLett.103.220601

K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Quantum dynamics of attractive versus repulsive bosonic Josephson junctions: Bose-Hubbard and full-Hamiltonian results, Physical Review A, vol.82, issue.1, p.13620, 2010.
DOI : 10.1103/PhysRevA.82.013620

D. Ciampini, O. Oliver, and E. Arimondo, QUANTUM CONTROL IN STRONGLY DRIVEN OPTICAL LATTICES, International Journal of Quantum Information, vol.09, issue.supp01, p.139, 2011.
DOI : 10.1142/S0219749911007150

A. Eckardt, T. Jinasundera, C. Weiss, and M. Holthaus, Analog of Photon-Assisted Tunneling in a Bose-Einstein Condensate, Physical Review Letters, vol.95, issue.20, 2005.
DOI : 10.1103/PhysRevLett.95.200401

H. J. Lipkin, N. Meshkov, and A. J. Glick, Validity of many-body approximation methods for a solvable model, Nuclear Physics, vol.62, issue.2, p.188, 1965.
DOI : 10.1016/0029-5582(65)90862-X

S. Ghose, R. Stock, P. Jessen, R. Lal, and A. Silberfarb, Chaos, entanglement, and decoherence in the quantum kicked top, Chaos, entanglement, and decoherence in the quantum kicked top, p.42318, 2008.
DOI : 10.1103/PhysRevA.78.042318

R. W. Spekkens and J. E. Sipe, Spatial fragmentation of a Bose-Einstein condensate in a double-well potential, Physical Review A, vol.59, issue.5, p.3868, 1999.
DOI : 10.1103/PhysRevA.59.3868

F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Atomic coherent states in quantum optics, Phys. Rev. A, vol.6, p.2212, 1972.

W. Zhang, D. H. Feng, and R. Gilmore, Coherent states: Theory and some applications, Reviews of Modern Physics, vol.62, issue.4, p.867, 1990.
DOI : 10.1103/RevModPhys.62.867

Y. P. Huang and M. G. Moore, Optimized Double-Well Quantum Interferometry with Gaussian Squeezed States, Physical Review Letters, vol.100, issue.25, p.250406, 2008.
DOI : 10.1103/PhysRevLett.100.250406

T. Kim, O. Pfister, M. J. Holland, J. Noh, and J. L. Hall, Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons, Physical Review A, vol.57, issue.5, p.4004, 1998.
DOI : 10.1103/PhysRevA.57.4004

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

P. Hyllus, O. Guhne, and A. Smerzi, Not all pure entangled states are useful for sub-shot-noise interferometry, Physical Review A, vol.82, issue.1, p.12337, 2010.
DOI : 10.1103/PhysRevA.82.012337

M. P. Fisher, P. W. Weichmann, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, AIP Conference Proceedings, p.546, 1989.
DOI : 10.1063/1.38820

S. Sachdev, Quantum Phase transitions, 1999.

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, Soviet Phys, JETP, vol.13, p.451, 1961.

G. Toth, C. Knapp, O. Gühne, and H. J. Briegel, Optimal Spin Squeezing Inequalities Detect Bound Entanglement in Spin Models, Physical Review Letters, vol.99, issue.25, p.250405, 2007.
DOI : 10.1103/PhysRevLett.99.250405

K. Eckert, J. Schliemann, D. Bruß, and M. Lewenstein, Quantum Correlations in Systems of Indistinguishable Particles, Quantum Correlations in Systems of Indistinguishable Particles, p.88, 2002.
DOI : 10.1006/aphy.2002.6268

F. Benatti, R. Floreanini, and U. Marzolino, Sub-shot-noise quantum metrology with entangled identical particles, Annals of Physics, vol.325, issue.4, p.924, 2010.
DOI : 10.1016/j.aop.2010.01.005

P. Hyllus, A. Smerzi, D. Schlenk, and H. Weinfurter, Sub shot-noise phase sensitivity with symmetrization-entanglement, preprint, 2011.

J. K. Korbicz, O. Gühne, M. Lewenstein, H. Häffner, C. F. Roos et al., -qubit systems: Theory and experiment, Physical Review A, vol.74, issue.5, p.52319, 2006.
DOI : 10.1103/PhysRevA.74.052319

URL : https://hal.archives-ouvertes.fr/hal-00879103

A. Sørensen and K. Mølmer, Entanglement and Extreme Spin Squeezing, Physical Review Letters, vol.86, issue.20, p.4431, 2001.
DOI : 10.1103/PhysRevLett.86.4431

G. Vitagliano, P. Hyllus, I. L. Egusquiza, and G. Toth, Optimal Spin Squeezing Inequalities Detect Bound Entanglement in Spin Models, 2011.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 2000.

C. Bodet, J. Estève, M. K. Oberthaler, and T. Gasenzer, Two-mode Bose gas: Beyond classical squeezing, Physical Review A, vol.81, issue.6, p.63605, 2010.
DOI : 10.1103/PhysRevA.81.063605

URL : http://arxiv.org/abs/1002.2504

T. Wei and P. M. Goldbart, Geometric measure of entanglement and applications to bipartite and multipartite quantum states, Physical Review A, vol.68, issue.4, p.42307, 2003.
DOI : 10.1103/PhysRevA.68.042307

M. Aulbach, D. Markham, and M. Murao, The maximally entangled symmetric state in terms of the geometric measure, New Journal of Physics, vol.12, issue.7, p.73025, 2010.
DOI : 10.1088/1367-2630/12/7/073025

J. Martin, O. Giraud, P. A. Braun, D. Braun, and T. Bastin, Multiqubit symmetric states with high geometric entanglement, Physical Review A, vol.81, issue.6, p.62347, 2010.
DOI : 10.1103/PhysRevA.81.062347

URL : https://hal.archives-ouvertes.fr/hal-00544423

W. Dür, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Physical Review A, vol.62, issue.6, p.62314, 2000.
DOI : 10.1103/PhysRevA.62.062314

S. Haroche, 4` eme leçon du cours 2006-2007, Cours auColì ege de France

L. Pezzé, L. A. Collins, A. Smerzi, G. P. Berman, and A. R. Bishop, Sub-shot-noise phase sensitivity with a Bose-Einstein condensate Mach-Zehnder interferometer, Physical Review A, vol.72, issue.4, p.43612, 2005.
DOI : 10.1103/PhysRevA.72.043612

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

J. I. Cirac, M. Lewenstein, K. Mølmer, and P. Zoller, Quantum superposition states of Bose-Einstein condensates, Physical Review A, vol.57, issue.2, p.1208, 1998.
DOI : 10.1103/PhysRevA.57.1208

T. Ho and C. V. Ciobanu, The Schr??dinger Cat Family in Attractive Bose Gases, Journal of Low Temperature Physics, vol.135, issue.3/4, p.257, 2004.
DOI : 10.1023/B:JOLT.0000024552.87247.eb

M. Kitagawa and Y. Yamamoto, Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer, Physical Review A, vol.34, issue.5, p.3974, 1986.
DOI : 10.1103/PhysRevA.34.3974

F. Piazza, L. Pezzé, and A. Smerzi, Macroscopic superpositions of phase states with Bose-Einstein condensates, Physical Review A, vol.78, issue.5, p.51601, 2008.
DOI : 10.1103/PhysRevA.78.051601

B. Yurke and D. Stoler, Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion, Physical Review Letters, vol.57, issue.1, p.13, 1986.
DOI : 10.1103/PhysRevLett.57.13

C. C. Gerry, Schr??dinger cat states in a Josephson junction, Physical Review B, vol.57, issue.13, p.7474, 1997.
DOI : 10.1103/PhysRevB.57.7474

M. W. Jack, Effect of atom loss on collapse and revivals of phase coherence in small atomic samples, Physical Review A, vol.67, issue.4, p.43612, 2003.
DOI : 10.1103/PhysRevA.67.043612

G. S. Agarwal, R. R. Puri, and R. P. Singh, Atomic Schr??dinger cat states, Atomic Schrödinger cat states, p.2249, 1997.
DOI : 10.1103/PhysRevA.56.2249

C. Weiss and N. Teichmann, -Particle Quantum Dynamics as a Signature of Entanglement, Physical Review Letters, vol.100, issue.14, p.140408, 2008.
DOI : 10.1103/PhysRevLett.100.140408

URL : https://hal.archives-ouvertes.fr/hal-01056931

V. O. Nesterenko, A. N. Novikov, A. Y. Cherny, F. F. De-souza-cruz, and E. Suraud, An adiabatic transport of Bose???Einstein condensates in double-well traps, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.42, issue.23, p.235303, 2009.
DOI : 10.1088/0953-4075/42/23/235303

URL : https://hal.archives-ouvertes.fr/hal-00990527

A. Micheli, D. Jaksch, J. I. Cirac, and P. Zoller, Many-particle entanglement in two-component Bose-Einstein condensates, Physical Review A, vol.67, issue.1, p.13607, 2003.
DOI : 10.1103/PhysRevA.67.013607

U. Boscain and B. Piccoli, Optimal syntheses for control systems on 2-D manifolds, 2004.

J. Werschnik and E. K. Gross, Quantum optimal control theory, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.40, issue.18, p.175, 2007.
DOI : 10.1088/0953-4075/40/18/R01

R. Gilmore, Wigner distribution on su(2) In Lecture Notes in Physics, 1987.

M. O. Scully and K. Wódkiewicz, Spin Quasi-distribution Functions, Foundation of, Physics, vol.24, p.85, 1994.

J. P. Dowling, G. S. Agarwal, and W. P. Schleich, Wigner distribution of a general angular-momentum state: Applications to a collection of two-level atoms, Physical Review A, vol.49, issue.5, p.4101, 1994.
DOI : 10.1103/PhysRevA.49.4101

S. M. Chumakov, A. B. Klimov, and K. B. Wolf, Connection between two Wigner functions for spin systems, Physical Review A, vol.61, issue.3, p.34101, 2000.
DOI : 10.1103/PhysRevA.61.034101

R. Schmied and P. Treutlein, Tomographic reconstruction of the Wigner function on the Bloch sphere, New Journal of Physics, vol.13, issue.6, 2011.
DOI : 10.1088/1367-2630/13/6/065019

S. M. Chumakov, A. Frank, and K. B. Wolf, Finite Kerr medium: Macroscopic quantum superposition states and Wigner functions on the sphere, Physical Review A, vol.60, issue.3, p.1817, 1999.
DOI : 10.1103/PhysRevA.60.1817

C. Lee and H. Jeong, Quantification of Macroscopic Quantum Superpositions within Phase Space, Physical Review Letters, vol.106, issue.22, p.220401, 2011.
DOI : 10.1103/PhysRevLett.106.220401

J. Gong, Comment on Quantification of Macroscopic Quantum Superpositions within Phase Space, 2011.

A. Kenfack and K. Zyczkowski, Negativity of the Wigner function as an indicator of non-classicality, Journal of Optics B: Quantum and Semiclassical Optics, vol.6, issue.10, p.396, 2004.
DOI : 10.1088/1464-4266/6/10/003

A. Biswas and G. S. Agarwal, Nonclassicality and decoherence of photon-subtracted squeezed states, Physical Review A, vol.75, issue.3, p.32104, 2007.
DOI : 10.1103/PhysRevA.75.032104

W. Schleich, M. Pernigo, and F. Le-kien, Nonclassical state from two pseudoclassical states, Physical Review A, vol.44, issue.3, p.2172, 1991.
DOI : 10.1103/PhysRevA.44.2172

R. L. Hudson, When is the wigner quasi-probability density non-negative?, Reports on Mathematical Physics, vol.6, issue.2, p.249, 1974.
DOI : 10.1016/0034-4877(74)90007-X

M. S. Kim, E. Park, P. L. Knight, and H. Jeong, Nonclassicality of a photon-subtracted Gaussian field, Physical Review A, vol.71, issue.4, p.43805, 2005.
DOI : 10.1103/PhysRevA.71.043805

W. Vogel, Nonclassical States: An Observable Criterion, Physical Review Letters, vol.84, issue.9, p.1849, 2000.
DOI : 10.1103/PhysRevLett.84.1849

T. Richter and W. Vogel, Observing the nonclassicality of a quantum state, Journal of Optics B: Quantum and Semiclassical Optics, vol.5, issue.3, p.371, 2003.
DOI : 10.1088/1464-4266/5/3/372

B. C. Sanders, Quantum dynamics of the nonlinear rotator and the effects of continual spin measurement, Physical Review A, vol.40, issue.5, p.2417, 1989.
DOI : 10.1103/PhysRevA.40.2417

T. J. Haigh, A. J. Ferris, and K. K. Olsen, Demonstrating mesoscopic superpositions in double-well Bose???Einstein condensates, Optics Communications, vol.283, issue.18, p.3540, 2010.
DOI : 10.1016/j.optcom.2010.04.067

F. Natterer, The Mathematics of Computerized Tomography, 1986.

E. W. Weisstein, Radon transform, 1987.

K. Vogel and H. Risken, Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase, Physical Review A, vol.40, issue.5, p.2847, 1989.
DOI : 10.1103/PhysRevA.40.2847

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune et al., Reconstruction of non-classical cavity field states with snapshots of their decoherence, Nature, vol.32, issue.7212, p.510, 2008.
DOI : 10.1038/nature07288

S. Haroche and J. M. Raimond, Exploring the quantum. Oxford Graduate texts, 2008.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Optics and interferometry with atoms and molecules, Reviews of Modern Physics, vol.81, issue.3, p.1051, 2009.
DOI : 10.1103/RevModPhys.81.1051

I. Tikhonenkov, M. G. Moore, and A. Vardi, Optimal Gaussian squeezed states for atom interferometry in the presence of phase diffusion, Physical Review A, vol.82, issue.4, p.43624, 2010.
DOI : 10.1103/PhysRevA.82.043624

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, Phase Detection at the Quantum Limit with Multiphoton Mach-Zehnder Interferometry, Physical Review Letters, vol.99, issue.22, p.223602, 2007.
DOI : 10.1103/PhysRevLett.99.223602

S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Physical Review Letters, vol.72, issue.22, p.3439, 1994.
DOI : 10.1103/PhysRevLett.72.3439

S. L. Braunstein, C. M. Caves, and G. J. Milburn, Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance, Generalized Uncertainty Relations: Theory , Examples, and Lorentz Invariance, p.135, 1996.
DOI : 10.1006/aphy.1996.0040

A. Uhlmann, The ???transition probability??? in the state space of a ???-algebra, Reports on Mathematical Physics, vol.9, issue.2, p.273, 1976.
DOI : 10.1016/0034-4877(76)90060-4

A. Smerzi, Zeno Dynamics and Distinguishability of Quantum States, 2010.

R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, and Q. Entanglement, Quantum entanglement, Reviews of Modern Physics, vol.81, issue.2, p.865, 2009.
DOI : 10.1103/RevModPhys.81.865

V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nature Photonics, vol.76, issue.4, 2011.
DOI : 10.1038/nphoton.2011.35

S. M. Giampaolo, G. Adesso, and F. Illuminati, Separability and ground-state factorization in quantum spin systems, Physical Review B, vol.79, issue.22, p.224434, 2009.
DOI : 10.1103/PhysRevB.79.224434

L. Amico and R. Fazio, Entanglement and magnetic order, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.50, p.504001, 2009.
DOI : 10.1088/1751-8113/42/50/504001

P. Zanardi, L. C. Venuti, and P. Giorda, Bures metric over thermal state manifolds and quantum criticality, Physical Review A, vol.76, issue.6, p.62318, 2007.
DOI : 10.1103/PhysRevA.76.062318

G. Mazzarella, L. Salasnich, A. Parola, and F. Toigo, Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schr??dinger cat states to separable Fock states, Physical Review A, vol.83, issue.5, p.53607, 2011.
DOI : 10.1103/PhysRevA.83.053607

J. Ma and X. Wang, Fisher information and spin squeezing in the Lipkin-Meshkov-Glick model, Physical Review A, vol.80, issue.1, p.12318, 2009.
DOI : 10.1103/PhysRevA.80.012318

R. Orùs, S. Dusuel, and J. Vidal, Equivalence of Critical Scaling Laws for Many-Body Entanglement in the Lipkin-Meshkov-Glick Model, Physical Review Letters, vol.101, issue.2, p.25701, 2008.
DOI : 10.1103/PhysRevLett.101.025701

U. Dorner, Quantum frequency estimation with trapped ions and atoms, New Journal of Physics, vol.14, issue.4, 2011.
DOI : 10.1088/1367-2630/14/4/043011

L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Physical Review A, vol.58, issue.4, p.2733, 1998.
DOI : 10.1103/PhysRevA.58.2733

E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch et al., Decoherence and the appearance of a Classical World in Quantum Theory, 1996.
DOI : 10.1007/978-3-662-05328-7

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1972.
DOI : 10.1119/1.1972842

A. Widera, F. Gerbier, S. Fölling, T. Gericke, O. Mandel et al., Coherent Collisional Spin Dynamics in Optical Lattices, Physical Review Letters, vol.95, issue.19, p.190405, 2005.
DOI : 10.1103/PhysRevLett.95.190405

URL : https://hal.archives-ouvertes.fr/hal-00116289

D. M. Stamper-kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye, H. Miesner et al., Optical Confinement of a Bose-Einstein Condensate, Optical Confinement of a Bose-Einstein Condensate, p.2027, 1998.
DOI : 10.1103/PhysRevLett.80.2027

M. W. Jack, Decoherence due to Three-Body Loss and its Effect on the State of a Bose-Einstein Condensate, Physical Review Letters, vol.89, issue.14, p.140402, 2002.
DOI : 10.1103/PhysRevLett.89.140402

A. Sinatra and Y. Castin, Phase dynamics of Bose-Einstein condensates: Losses versus revivals, The European Physical Journal D - Atomic, Molecular and Optical Physics, vol.4, issue.3, p.247, 1998.
DOI : 10.1007/s100530050206

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell et al., Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay, Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay, p.337, 1997.
DOI : 10.1103/PhysRevLett.79.337

K. Pawlovski and K. Rzazewski, Background atoms and decoherence in optical lattices, Physical Review A, vol.81, issue.1, p.13620, 2010.
DOI : 10.1103/PhysRevA.81.013620

Y. Lin, Y. Castin, and A. Sinatra, Optimum Spin squeezing in Bose-Einstein Condensates with particle losses, Phys. Rev. Lett, vol.100, p.210401, 2008.

P. Hyllus, L. Pezzé, and A. Smerzi, Entanglement and Sensitivity in Precision Measurements with States of a Fluctuating Number of Particles, Physical Review Letters, vol.105, issue.12, p.120501, 2010.
DOI : 10.1103/PhysRevLett.105.120501

URL : https://hal.archives-ouvertes.fr/hal-00746823

R. Bach and K. Rzazewski, Correlations in Atomic Systems: Diagnosing Coherent Superpositions, Physical Review Letters, vol.92, issue.20, 2004.
DOI : 10.1103/PhysRevLett.92.200401

URL : http://arxiv.org/abs/cond-mat/0403553

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

Y. Hao and Q. Gu, Dynamics of two-component Bose-Einstein condensates coupled with the environment, Physical Review A, vol.83, issue.4, p.43620, 2011.
DOI : 10.1103/PhysRevA.83.043620

M. Greiner, O. Mandel, T. W. Hansch, 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

N. Bar-gill, C. Gross, I. Mazets, M. Oberthaler, and G. Kurizki, Einstein-Podolsky-Rosen Correlations of Ultracold Atomic Gases, Physical Review Letters, vol.106, issue.12, p.120404, 2011.
DOI : 10.1103/PhysRevLett.106.120404

Q. Y. He, M. D. Reid, T. G. Vaughan, C. Gross, M. Oberthaler et al., Einstein-Podolsky-Rosen Entanglement Strategies in Two-Well Bose-Einstein Condensates, Physical Review Letters, vol.106, issue.12, p.120405, 2011.
DOI : 10.1103/PhysRevLett.106.120405

K. Molmer, Y. Castin, and J. Dalibard, Monte Carlo wave-function method in quantum optics, Journal of the Optical Society of America B, vol.10, issue.3, p.524, 1993.
DOI : 10.1364/JOSAB.10.000524