Elementary and topological excitations in ultracold dipolar Bose gases

PhD ThesisQ uantum gases are an exemplar for exploring quantum phenomena; dipolar quantum gases only enriches the pool of potential experiments, exhibiting long-range and anisotropic interactions. In this thesis, we perform extensive numerical and theoretical studies of the dipolar Gross-Pitaevskii equation, exposing new intriguing phenomena of solitons and vortices in these systems. Firstly, we map out the stability diagram as a function of strength and polarisation direction of the atomic dipoles in a quasi-one-dimensional dipolar gas, identifying both roton and phonon instabilities. Then we obtain the family of dark soliton solutions supported in this system. Away from these instabilities dark solitons collide elastically. Varying the polarisation direction relative to the condensate axis enables tuning of this nonlocal interaction between repulsive and attractive; the latter case supports unusual dark soliton bound states. Remarkably, these bound states are themselves shown to behave like solitons, emerging unscathed from collisions with each other. In trapped gases the oscillation frequency of the dark soliton is strongly dependent on the atomic interactions, in stark contrast to the non-dipolar case. Considering parameter regimes allowing the existence of bright solitons we map out the existence of the soliton solutions and show three collisional regimes: free collisions, bound state formation and soliton fusion. We examine the solitons in their full three-dimensional form through a variational approach; along with regimes of instability to collapse and runaway expansion, we identify regimes of stability which are accessible to current experiments. Then, we undertake a theoretical analysis of the stability of a Thomas-Fermi density pro le for a dipolar gas in a rotating frame of reference and nd that the theoretical prediction for "anti-dipoles" is only experimentally realisable for short periods of time. We compare this theory against numerical simulations of the governing equation for these systems and nd excellent agreement. Finally, we study the elementary characteristics of turbulence in a quantum ferro uid through the context of a dipolar Bose gas condensing from a highly non-equilibrium thermal state. Our simulations reveal that the dipolar interactions drive the emergence of polarised turbulence and density corrugations. The super uid vortex lines and density uctuations adopt a columnar or strati ed con guration, with the vortices tending to form in the low density regions to minimise kinetic energy. When the interactions are dominantly dipolar, the decay rate of vortex line length is enhanced. This system poses exciting prospects for realising strati ed quantum turbulence and new levels of generating and controlling turbulence using magnetic elds.EPSR