H. Lignier, C. Sias, D. Ciampini, Y. Singh, A. Zenesini et al., Dynamical Control of Matter-Wave Tunneling in Periodic Potentials, Physical Review Letters, vol.99, issue.22, p.220403, 2007.
DOI : 10.1103/PhysRevLett.99.220403

D. N. Basov, R. D. Averitt, D. Van-der-marel, M. Dressel, and K. Haule, Electrodynamics of correlated electron materials, Reviews of Modern Physics, vol.83, issue.2, p.471, 2011.
DOI : 10.1103/RevModPhys.83.471

J. Struck, C. Lschlger, R. Le-targat, P. Soltan-panahi, A. Eckardt et al., Quantum Simulation of Frustrated Classical Magnetism in Triangular Optical Lattices, Science, vol.333, issue.6045, p.996, 2011.
DOI : 10.1126/science.1207239

J. T. Barreiro, M. Mller, P. Schindler, D. Nigg, T. Monz et al., An open-system quantum simulator with trapped ions, Nature, vol.4, issue.7335, p.486, 2010.
DOI : 10.1038/nature09801

N. Syassen, D. M. Bauer, M. Lettner, T. Volz, D. Dietze et al., Strong Dissipation Inhibits Losses and Induces Correlations in Cold Molecular Gases, Science, vol.320, issue.5881, p.1329, 2008.
DOI : 10.1126/science.1155309

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

C. Hung, X. Zhang, N. Gemelke, and C. Chin, Slow Mass Transport and Statistical Evolution of an Atomic Gas across the Superfluid???Mott-Insulator Transition, Physical Review Letters, vol.104, issue.16, p.160403, 2010.
DOI : 10.1103/PhysRevLett.104.160403

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch et al., Single-atom-resolved fluorescence imaging of an atomic Mott insulator, Nature, vol.78, issue.7311, p.68, 2010.
DOI : 10.1038/nature09378

URL : https://hal.archives-ouvertes.fr/hal-01397842

W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon et al., Probing the Superfluid-to-Mott Insulator Transition at the Single-Atom Level, Science, vol.329, issue.5991, p.547, 2010.
DOI : 10.1126/science.1192368

D. Chen, M. White, C. Borries, and B. Demarco, Quantum Quench of an Atomic Mott Insulator, Physical Review Letters, vol.106, issue.23, p.235304, 2011.
DOI : 10.1103/PhysRevLett.106.235304

A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, : Nonequilibrium dynamics of closed interacting quantum systems, Reviews of Modern Physics, vol.83, issue.3, p.863, 2011.
DOI : 10.1103/RevModPhys.83.863

F. M. Cucchietti, B. Damski, J. Dziarmaga, and W. H. Zurek, Dynamics of the Bose-Hubbard model: Transition from a Mott insulator to a superfluid, Physical Review A, vol.75, issue.2, p.23603, 2007.
DOI : 10.1103/PhysRevA.75.023603

L. Cincio, J. Dziarmaga, M. M. Rams, and W. H. Zurek, Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model, Physical Review A, vol.75, issue.5, p.52321, 2007.
DOI : 10.1103/PhysRevA.75.052321

R. W. Cherng and L. S. Levitov, Entropy and correlation functions of a driven quantum spin chain, Physical Review A, vol.73, issue.4, p.43614, 2006.
DOI : 10.1103/PhysRevA.73.043614

A. Polkovnikov and V. Gritsev, Breakdown of the adiabatic limit in low-dimensional gapless systems, Nature Physics, vol.66, issue.6, p.477, 2008.
DOI : 10.1038/nphys963

M. Eckstein and M. Kollar, Near-adiabatic parameter changes in correlated systems: influence of the ramp protocol on the excitation energy, New Journal of Physics, vol.12, issue.5, p.55012, 2010.
DOI : 10.1088/1367-2630/12/5/055012

M. Moeckel and S. Kehrein, Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics, New Journal of Physics, vol.12, issue.5, p.55016, 2010.
DOI : 10.1088/1367-2630/12/5/055016

B. Dóra, M. Haque, and G. Zaránd, Crossover from Adiabatic to Sudden Interaction Quench in a Luttinger Liquid, Physical Review Letters, vol.106, issue.15, p.156406, 2011.
DOI : 10.1103/PhysRevLett.106.156406

J. Dziarmaga and M. Tylutki, Excitation energy after a smooth quench in a Luttinger liquid, Physical Review B, vol.84, issue.21, pp.214522-013615, 2011.
DOI : 10.1103/PhysRevB.84.214522

E. H. Lieb and D. W. Robinson, The finite group velocity of quantum spin systems, Communications in Mathematical Physics, vol.7, issue.3, p.251, 1972.
DOI : 10.1007/BF01645779

P. Calabrese and J. Cardy, Time Dependence of Correlation Functions Following a Quantum Quench, Physical Review Letters, vol.96, issue.13, p.136801, 2006.
DOI : 10.1103/PhysRevLett.96.136801

M. Cheneau, P. Barmettler, D. Poletti, M. Endres, P. Schauß et al., Light-cone-like spreading of correlations in a quantum many-body system, Nature, vol.98, issue.7382, p.484, 2012.
DOI : 10.1038/nature10748

URL : https://hal.archives-ouvertes.fr/hal-01397832

M. A. Cazalilla, Effect of Suddenly Turning on Interactions in the Luttinger Model, Physical Review Letters, vol.97, issue.15, p.156403, 2006.
DOI : 10.1103/PhysRevLett.97.156403

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

C. Kollath, U. Schollwöck, J. Delft, and W. Zwerger, Spatial correlations of trapped one-dimensional bosons in an optical lattice, Physical Review A, vol.69, issue.3, p.31601, 2004.
DOI : 10.1103/PhysRevA.69.031601

T. Giamarchi, Quantum Physics in One Dimension, 2004.
DOI : 10.1093/acprof:oso/9780198525004.001.0001

M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. , One dimensional bosons: From condensed matter systems to ultracold gases, Reviews of Modern Physics, vol.83, issue.4, p.1405, 2011.
DOI : 10.1103/RevModPhys.83.1405

URL : https://hal.archives-ouvertes.fr/ensl-00647350

E. H. Lieb and W. Liniger, Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Physical Review, vol.130, issue.4, p.1605, 1963.
DOI : 10.1103/PhysRev.130.1605

T. D. Kühner and H. Monien, Phases of the one-dimensional Bose-Hubbard model, Physical Review B, vol.58, issue.22, p.14741, 1998.
DOI : 10.1103/PhysRevB.58.R14741

F. D. Haldane, Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids, Physical Review Letters, vol.47, issue.25, p.1840, 1981.
DOI : 10.1103/PhysRevLett.47.1840

J. Bernier, R. Citro, C. Kollath, and E. Orignac, Supplementary material for Correlation dynamics during a slow interaction quench in a one-dimensional Bose gas, 2013.

S. Bravyi, M. B. Hastings, and F. Verstraete, Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order, Physical Review Letters, vol.97, issue.5, p.50401, 2006.
DOI : 10.1103/PhysRevLett.97.050401

A. Mitra, Correlation functions in the prethermalized regime after a quantum quench of a spin chain, Physical Review B, vol.87, issue.20, p.205109, 2013.
DOI : 10.1103/PhysRevB.87.205109

C. Karrasch, J. Rentrop, D. Schuricht, and V. Meden, Luttinger-liquid universality in the time evolution after an interaction quench, Physical Review Letters, vol.109, issue.12, p.126406, 2012.
DOI : 10.1103/PhysRevLett.109.126406

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

B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling et al., Tonks???Girardeau gas of ultracold atoms in an optical lattice, Nature, vol.42, issue.6989, p.277, 2004.
DOI : 10.1103/PhysRevLett.90.150402

URL : https://hal.archives-ouvertes.fr/hal-00002239

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

]. S. Ritter, A. Ottl, T. Donner, T. Bourdel, M. Köhl et al., Observing the Formation of Long-Range Order during Bose-Einstein Condensation, Physical Review Letters, vol.98, issue.9, p.90402, 2007.
DOI : 10.1103/PhysRevLett.98.090402

T. Donner, S. Ritter, T. Bourdel, A. Ottl, M. Köhl et al., Critical Behavior of a Trapped Interacting Bose Gas, Science, vol.315, issue.5818, p.1556, 2007.
DOI : 10.1126/science.1138807

S. S. Natu, K. R. Hazzard, and E. J. Mueller, Local Versus Global Equilibration near the Bosonic Mott-Insulator???Superfluid Transition, Physical Review Letters, vol.106, issue.12, p.125301, 2011.
DOI : 10.1103/PhysRevLett.106.125301

A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, Bose-Einstein Condensation of Atoms in a Uniform Potential, Physical Review Letters, vol.110, issue.20, p.200406, 2013.
DOI : 10.1103/PhysRevLett.110.200406

P. Barmettler, D. Poletti, M. Cheneau, and C. Kollath, Propagation front of correlations in an interacting Bose gas, Physical Review A, vol.85, issue.5, p.53625, 2012.
DOI : 10.1103/PhysRevA.85.053625

URL : https://hal.archives-ouvertes.fr/hal-01397829