Dynamical properties of Bose-Bose Mixtures

In this Thesis is presented a study on dynamical properties of mixtures of ultraold Bose gases. The behaviour of this system in different regimes is analysed: with and without coherent coupling between the two components, in homogeneous and harmonic shaped trapping potentials and in different dimensions and geometries. Most of the results presented here have been obtained by means of numerical solutions of coupled Gross-Pitaevskii equations and have been compared with theoretical predictions (and sometimes experiments), describing the same phenomena. In particualr the stability of persistent currents in a two-component Bose-Einstein condensate in a toroidal trap is studied in both the miscible and the immiscible regime. In the miscible regime we show that superflow decay is related to linear instabilities of the spin-density Bogoliubov mode. We find a region of partial stability, where the flow is stable in the majority component while it decays in the minority component. We also characterize the dynamical instability appearing for a large relative velocity between the two components. In the immiscible regime the stability criterion is modified and depends on the specific density distribution of the two components. The effect of a coherent coupling between the two components is also discussed. A study on the collective modes of the minority component of a highly unbalanced Bose-Bose mixture is also presented. In the immiscible case we find that the ground state can be a two-domain walls soliton. Although the mode frequencies are continuous at the transition, their behaviour is very different with respect to the miscible case. The dynamical behaviour of the solitonic structure and the frequency dependence on the inter- and intra-species interaction is numerically studied using coupled Gross-Pitaevskii equations. The results of the study on the static and the dynamic response of coherently coupled two component Bose-Einstein condensates due to a spin-dipole perturbation is also sown. The static dipole susceptibility is determined and is shown to be a key quantity to identify the second order ferromagnetic transition occurring at large inter-species interactions. The dynamics, which is obtained by quenching the spin-dipole perturbation, is very much affected by the system being paramagnetic or ferromagnetic and by the correlation between the motional and the internal degrees of freedom. In the paramagnetic phase the gas exhibits well defined out-of-phase dipole oscillations, whose frequency can be related to the susceptibility of the system using a sum rule approach. In particular in the interaction SU (2) symmetric case, when all the two-body interactions are the same, the external dipole oscillation coincides with the internal Rabi flipping frequency. In the ferromagnetic case, where linear response theory is not applicable, the system shows highly non-linear dynamics. In particular we observe phenomena related to ground state selection: the gas, initially trapped in a domain wall configuration, reaches a final state corresponding to the magnetic ground state plus small density ripples. Interestingly, the time during which the gas is unable to escape from its initial configuration is found to be proportional to the square root of the wall surface tension.