Bright solitons in quasi-one dimensional dipolar condensates with spatially modulated interactions

We introduce a model for the condensate of dipolar atoms or molecules, in which the dipole-dipole interaction (DDI) is periodically modulated in space, due to a periodic change of the local orientation of the permanent dipoles, imposed by the corresponding structure of an external field (the necessary field can be created, in particular, by means of magnetic lattices, which are available to the experiment). The system represents a realization of a nonlocal nonlinear lattice, which has a potential to support various spatial modes. By means of numerical methods and variational approximation (VA), we construct bright one-dimensional solitons in this system, and study their stability. In most cases, the VA provides good accuracy, and correctly predicts the stability by means of the Vakhitov-Kolokolov (VK)\ criterion. It is found that the periodic modulation may destroy some solitons, which exist in the usual setting with unmodulated DDI, and can create stable solitons in other cases, not verified in the absence of modulations. Unstable solitons typically transform into persistent localized breathers. The solitons are often mobile, with inelastic collisions between them leading to oscillating localized modes.Comment: To appear in Physical Review A (2013). 24 pages (preprint format), 13 figure

Faraday waves on a bubble Bose-Einstein condensed binary mixture

By studying the dynamic stability of Bose-Einstein condensed binary mixtures trapped on the surface of an ideal two-dimensional spherical bubble, we show how the Rabi coupling between the species can modulate the interactions leading to parametric resonances. In this spherical geometry, the discrete unstable angular modes drive both phase separations and spatial patterns, with Faraday waves emerging and coexisting with an immiscible phase. Noticeable is the fact that, in the context of discrete kinetic energy spectrum, the only parameters to drive the emergence of Faraday waves are the $s-wave$ contact interactions and the Rabi coupling. Once analytical solutions for population dynamics are obtained, the stability of homogeneous miscible species is investigated through Bogoliubov-de Gennes and Floquet methods, with predictions being analysed by full numerical solutions applied to the corresponding time-dependent coupled formalism.Comment: 17 pages, 15 figure

Expansion and correlation dynamics of interacting bosons released from a harmonic trap

We investigate the expansion dynamics of one-dimensional strongly interacting bosons released from a harmonic trap from the first principle. We utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) to solve the many-body Schr\"odinger equation at high level of accuracy as the MCTDHB basis sets are explicitly time dependent and optimised by variational principle. We probe the expansion dynamics for very strong interaction but not in Tonks-Girardeau (TG) limit and thus integrability breaks down. We characterize the dynamics by measure of expansion radius and expansion velocity. We find that for an wide range of strong interaction strength, the expansion dynamics is trimodal. We present three different time-scales of expansion -- inner-core, outer-core and the whole cloud; whereas for non-interacting case, it is unimodal. We also report the dynamics of higher-body densities and correlations and observe the antibunching effect. The two- and three-body densities are characterized by the appearance of correlation hole along the diagonal due to very strong interaction that mimics the Pauli principle. With the expansion of bosons the correlation hole also spread. We also report the expansion dynamics of 1D dipolar bosons released from the trap. When very strong contact interaction leads to fermionization limit, for strongly interacting dipolar bosons lead to crystal phase. The expansion dynamics of dipolar bosons is again trimodal as before, but the expansion velocity is much larger and diverging unlike the case of contact interaction where the expansion velocity is converged. The diverging expansion dynamics is further supported by the unbounded energy for long range interaction.Comment: 10 pages, 11 figure