Nonequilibrium dynamics of strongly correlated one-dimensional ultracold quantum gases

In the original work of this Thesis we use Time Dependent Density Matrix Renormalization Group (TDMRG) to follow and study the unitary dynamics of 1D strongly interacting quantum systems. In the rest part we present our work on the collision of spin polarized fermionic clouds. We study spin drag e ects immediately after the collision. This work is relevant to current experiments where pure spin currents have been realized with ultracold atomic gases. Several of our predictions can be veri ed in future experiments on strongly interacting few-fermion systems. In the second part the highly imbalanced case of an impurity immersed in a bath of bosonic atoms is considered. The interaction of the impurity with the bath manifests in the mass renormalization and in the damping of the oscillations of the breathing mode of the impurity in a harmonic potential. We compare the TDMRG results with an analytically tractable model in which the bath is treated as a Luttinger liquid and pinpoint striking deviations from this picture due to the nonlinear nature of the Lieb-Liniger gas. This results are relevant to current and future experiments on impurities coupled to one-dimensional ultracold gases. Finally, we employ DMRG to study spin-orbit coupled bosons in 1D optical lattices, following recent remarkable experimental advances on arti cially engineered gauge elds and spin-orbit coupling in ultracold atoms. We concentrate in the Mott insulator region of the phase diagram of pseudospin-1/2 bosons with spin-orbit coupling and anisotropic interaction terms that fully break spin rotational symmetry