Ground-state energy and depletions for a dilute binary Bose gas

When calculating the ground-state energy of a weakly interacting Bose gas with the help of the customary contact pseudopotential, one meets an artifical ultraviolet divergence which is caused by the incorrect treatment of the true interparticle interactions at small distances. We argue that this problem can be avoided by retaining the actual, momentum-dependent interaction matrix elements, and use this insight for computing both the ground-state energy and the depletions of a binary Bose gas mixture. Even when considering the experimentally relevant case of equal masses of both species, the resulting expressions are quite involved, and they are no straightforward generalizations of the known single-species formulas. On the other hand, we demonstrate in detail how these latter formulas are recovered from our two-species results in the limit of vanishing interspecies interaction.