We investigate the mean-field equilibrium solutions for a two-species immiscible Bose-Einstein condensate confined by a harmonic confinement with additional linear perturbations. We observe a range of equilibrium density structures, including ball and shell formations and axially or radially separated states, with a marked sensitivity to the potential perturbations and the relative atom number in each species. Incorporation of linear trap perturbations, albeit weak, are found to be essential to match the range of equilibrium density profiles observed in a recent
87Rb-
133Cs Bose-Einstein condensate experiment [McCarron et al., Phys. Rev. A 84, 011603(R) (2011)]. Our analysis of this experiment demonstrates that sensitivity to linear trap perturbations is likely to be an important factor in interpreting the results of similar experiments in the future.
We report the formation of a dual-species Bose-Einstein condensate of
87Rb and
133Cs in the same trapping potential. Our method exploits the efficient sympathetic cooling of
133Cs via elastic collisions with
87Rb, initially in a magnetic quadrupole trap and subsequently in a levitated optical trap. The two condensates each contain up to $2\ifmmode\times\else\texttimes\fi{}{10}^{4}$ atoms and exhibit a striking phase separation, revealing the mixture to be immiscible due to strong repulsive interspecies interactions. Sacrificing all the
87Rb during the cooling, we create single-species
133Cs condensates of up to $6\ifmmode\times\else\texttimes\fi{}{10}^{4}$ atoms.
A Faraday-wave-like parametric instability is investigated via mean-field and Floquet analysis in immiscible binary Bose-Einstein condensates. The condensates form a so-called ball-shell structure in a two-dimensional harmonic trap. To trigger the dynamics, the scattering length of the core condensate is periodically modulated in time. We reveal that in the dynamics the interface becomes unstable towards the formation of oscillating patterns. The interface oscillates subharmonically, exhibiting an
m-fold rotational symmetry that can be controlled by maneuvering the amplitude and the frequency of the modulation. Using Floquet analysis we are able to predict the generated interfacial tension of the mixture and derive a dispersion relation for the natural frequencies of the emergent patterns. A heteronuclear system composed of $^{87}\mathrm{Rb}\ensuremath{-}^{85}\mathrm{Rb}$ atoms can be used for the experimental realization of the phenomenon, yet our results are independent of the specifics of the employed atomic species and of the parameters such as scattering lengths and trap strengths at which the driving is applied.