Structure formation in immiscible two--species Bose--Einstein condensates in perturbed harmonic traps

We investigate the mean--field equilibrium solutions for a trapped two--species $^{87}$Rb--$^{133}$Cs immiscible Bose--Einstein condensate, and show that the density profiles observed in a recent Bose-Einstein experiment (D. J. McCarron \emph{et al.} Phys. Rev. A 84, 011603 (2011)), which include ball and shell formations and axially/radially separated states, can be reproduced when accounting for weak linear perturbations. We also demonstrate the importance of the coupled growth of the two condensates by a simple finite temperature model which reveals such structures to be generally metastable in the presence of dissipation, with our findings confirmed by the more accurate Stochastic Projected Gross--Pitaevskii equation.