Abstract
We provide Monte Carlo simulation and analytic interface arguments for the absence of cylindrical symmetry in the density difference of a binary mixture of Bose-Einstein condensates in traps in the phase segregated regime. For different spin states of 87Rb, the total density remains very symmetric however. There is a metastable symmetric phase in a substantial part of this phase segregated regime. The boundary between the symmetric and the nonsymmetric phase is a function of the relative concentration. The effect of different confining potentials is investigated.