K. Osterloh, M. Baig, L. Santos, P. Zoller, and M. Lewenstein, Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter "Moth" to Lattice Gauge Theory, Physical Review Letters, vol.95, issue.1, p.10403, 2005.
DOI : 10.1103/PhysRevLett.95.010403

J. Ruseckas, G. Juzeli¯-unas, P. Ohberg, and M. Fleischhauer, Non-Abelian Gauge Potentials for Ultracold Atoms with Degenerate Dark States, Physical Review Letters, vol.95, issue.1, p.10404, 2005.
DOI : 10.1103/PhysRevLett.95.010404

Y. Lin, K. Jimenez-garcia, and I. B. Spielman, Spin???orbit-coupled Bose???Einstein condensates, Nature, vol.79, issue.7336, p.83, 2011.
DOI : 10.1038/nature09887

V. Galitski and I. B. Spielman, Spin???orbit coupling in quantum gases, Nature, vol.109, issue.7435, p.49, 2013.
DOI : 10.1038/nature11841

M. Kardar, Josephson-junction ladders and quantum fluctuations, Physical Review B, vol.33, issue.5, p.3125, 1986.
DOI : 10.1103/PhysRevB.33.3125

E. Granato, Phase transitions in Josephson-junction ladders in a magnetic field, Physical Review B, vol.42, issue.7, p.4797, 1990.
DOI : 10.1103/PhysRevB.42.4797

Y. Nishiyama, Finite-size-scaling analyses of the chiral ordert in the Josephson-junction ladder with half a flux quantum per plaquette, The European Physical Journal B, vol.17, issue.2, p.295, 2000.
DOI : 10.1007/s100510070144

E. Orignac and T. Giamarchi, Meissner effect in a bosonic ladder, Physical Review B, vol.64, issue.14, p.144515, 2001.
DOI : 10.1103/PhysRevB.64.144515

URL : https://hal.archives-ouvertes.fr/hal-00138243

M. C. Cha and J. G. Shin, Two peaks in the momentum distribution of bosons in a weakly frustrated two-leg optical ladder, Physical Review A, vol.83, issue.5, p.55602, 2011.
DOI : 10.1103/PhysRevA.83.055602

V. L. Pokrovsky and A. L. Talapov, Ground State, Spectrum, and Phase Diagram of Two-Dimensional Incommensurate Crystals, Physical Review Letters, vol.42, issue.1, p.65, 1979.
DOI : 10.1103/PhysRevLett.42.65

P. A. Bobbert, R. Fazio, G. Schön, and G. T. Zimanyi, Phase transitions in dissipative Josephson chains, Physical Review B, vol.41, issue.7, p.4009, 1990.
DOI : 10.1103/PhysRevB.41.4009

M. Atala, M. Aidelsburger, M. Lohse, J. Barreiro, B. Paredes et al., Observation of chiral currents with ultracold atoms in bosonic ladders, Nature Physics, vol.334, issue.8, p.588, 2014.
DOI : 10.1038/nphys2998

A. Petrescu and K. L. Hur, Bosonic Mott Insulator with Meissner Currents, Physical Review Letters, vol.111, issue.15, p.150601, 2013.
DOI : 10.1103/PhysRevLett.111.150601

URL : http://arxiv.org/abs/1306.5986

A. Dhar, M. Maji, T. Mishra, R. V. Pai, S. Mukerjee et al., Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state, Physical Review A, vol.85, issue.4, pp.41602-174501, 2012.
DOI : 10.1103/PhysRevA.85.041602

D. Hügel and B. Paredes, Chiral ladders and the edges of quantum Hall insulators, Physical Review A, vol.89, issue.2, p.23619, 2014.
DOI : 10.1103/PhysRevA.89.023619

A. Tokuno and A. Georges, Ground states of a Bose???Hubbard ladder in an artificial magnetic field: field-theoretical approach, New Journal of Physics, vol.16, issue.7, p.73005, 2014.
DOI : 10.1088/1367-2630/16/7/073005

M. Piraud, Z. Cai, I. P. Mcculloch, and U. Schollwöck, Quantum magnetism of bosons with synthetic gauge fields in one-dimensional optical lattices: A density-matrix renormalization-group study, Physical Review A, vol.89, issue.6, p.63618, 2014.
DOI : 10.1103/PhysRevA.89.063618

L. Barbiero, M. Abad, and A. Recati, Magnetic phase transition in coherently coupled Bose gases in optical lattices, Physical Review A, vol.93, issue.3, pp.1403-4185, 2014.
DOI : 10.1103/PhysRevA.93.033645

Z. Xu, W. Cole, and S. Zhang, Mott-superfluid transition for spin-orbit-coupled bosons in one-dimensional optical lattices, Physical Review A, vol.89, issue.5, p.51604, 2014.
DOI : 10.1103/PhysRevA.89.051604

J. Zhao, S. Hu, J. Chang, F. Zheng, P. Zhang et al., Evolution of magnetic structure driven by synthetic spin-orbit coupling in a two-component Bose-Hubbard model, Physical Review B, vol.90, issue.8, p.85117, 2014.
DOI : 10.1103/PhysRevB.90.085117

C. Hamner, Y. Zhang, M. Khamehchi, M. J. Davis, and P. Engels, Spin-Orbit-Coupled Bose-Einstein Condensates in a One-Dimensional Optical Lattice, Physical Review Letters, vol.114, issue.7, 2014.
DOI : 10.1103/PhysRevLett.114.070401

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

F. Crépin, N. Laflorencie, G. Roux, and P. Simon, Phase diagram of hard-core bosons on clean and disordered two-leg ladders: Mott insulator???Luttinger liquid???Bose glass, Physical Review B, vol.84, issue.5, p.54517, 2011.
DOI : 10.1103/PhysRevB.84.054517

A. Luther, Quantum solitons in one-dimensional conductors, Physical Review B, vol.15, issue.1, p.403, 1977.
DOI : 10.1103/PhysRevB.15.403

S. R. White, Density-matrix algorithms for quantum renormalization groups, Physical Review B, vol.48, issue.14, p.10345, 1993.
DOI : 10.1103/PhysRevB.48.10345

U. Schollwöck, The density-matrix renormalization group, Reviews of Modern Physics, vol.77, issue.1, p.259, 2005.
DOI : 10.1103/RevModPhys.77.259

D. Senechal, An introduction to bosonization, Theoretical Methods for Strongly Correlated Electrons CRM Series in Mathematical Physics, 2003.

M. A. Cazalilla, Bosonizing one-dimensional cold atomic gases, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.37, issue.7, p.1, 2004.
DOI : 10.1088/0953-4075/37/7/051

URL : http://arxiv.org/abs/cond-mat/0307033