Domain wall suppression in trapped mixtures of Bose-Einstein condensates

The ground state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial densities the energy can be computed by explicitly taking into account the normalization condition. This yields analytical results and provides the basis for further improvement of the approximation. As a case study, we consider a binary mixture of $^{87}$Rb atoms in two different hyperfine states in a double well potential and discuss the energy crossing between density profiles with different numbers of domain walls, as the number of particles and the inter-species interaction vary.