Effect of the interspecies interaction on the density profiles of miscible two-species Bose-Einstein condensates

We study harmonically trapped two-species Bose-Einstein condensates within the Gross-Pitaevskii formalism. By invoking the Thomas-Fermi approximation, we derive an analytical solution for the miscible ground state in a particular region of the system's parameter space. This solution furnishes a simple formula that relates the interspecies interaction strength to the second spatial moments of the density distribution of the minority condensate species. Accompanying numerical simulations confirm the accuracy of the solution and the interaction strength formula for sufficiently large numbers of condensed particles. The introduced formula may provide an additional scheme for determining interspecies scattering lengths that complements existing methods, such as those based on collective-excitation spectroscopy of the two-species condensates or on collisional measurements on thermal samples.