Ground State of Binary Condensates in harmonic and lattice potentials with variational ansatz

We propose an ansatz to study binary condensates, trapped in harmonic and optical lattice potentials, both in miscible and immiscible domains. The ansatz is an apt one for two reasons. First, it leads to the smooth transition from miscible to immiscible domains without any apriori assumptions. And second, unlike other ansatz proposed in the literature, its applicability is not constrained by interaction strengths and nature of the trapping potential. We varify the validity of the ansatz with Gram-Charlier expansion as an entirely indepedent measure based on the numerical results. In optical lattice potentials, we analyze the squeezing of the density profiles, due to the increase in the depth of the optical lattice potential. For this we develope a model with three potential wells, and define the relationship between the lattice depth and profile of the condensate.