Coherent cross-talk and parametric driving of matter-wave vortices

We show that the interaction between vortices and sound waves in atomic Bose-Einstein condensates can be elucidated in a double-well trap: with one vortex in each well, the sound emitted by each precessing vortex can be driven into the opposing vortex (if of the same polarity). This cross-talk leads to a periodic exchange of energy between the vortices which is long-range and highly efficient. The increase in vortex energy (obtained by numerical simulations of the Gross-Pitaevskii equation) is significant and experimentally observable as a migration of the vortex to higher density over just a few precession periods. Similar effects can be controllably engineered by introducing a precessing localised obstacle into one well as an artificial generator of sound, thereby demonstrating the parametric driving of energy into a vortex.Comment: 12 pages, 13 figure

Structure formation during the collapse of a dipolar atomic Bose-Einstein condensate

We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the Thomas-Fermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the non-adiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyse the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.Comment: In this version (the published version) we have slightly rewritten the manuscript in places and have corrected some typos. 15 pages and 13 figure

p-Wave stabilization of three-dimensional Bose-Fermi solitons

We explore bright soliton solutions of ultracold Bose-Fermi gases, showing that the presence of p-wave interactions can remove the usual collapse instability and support stable soliton solutions that are global energy minima. A variational model that incorporates the relevant s- and p-wave interactions in the system is established analytically and solved numerically to probe the dependencies of the solitons on key experimental parameters. Under attractive s-wave interactions, bright solitons exist only as meta-stable states susceptible to collapse. Remarkably, the presence of repulsive p-wave interactions alleviates this collapse instability. This dramatically widens the range of experimentally-achievable soliton solutions and indicates greatly enhanced robustness. While we focus specifically on the boson-fermion pairing of 87Rb and 40K, the stabilization inferred by repulsive p-wave interactions should apply to the wider remit of ultracold Bose-Fermi mixtures.Comment: 9 pages, 6 figure