Suppression of the quantum collapse in binary bosonic gases

Attraction of the quantum particle to the center in three-dimensional space with potential -V₀r^-2 gives rise to the quantum collapse, i.e., nonexistence of the ground state (GS) when the attraction strength exceeds a critical value [(_V0(cr))1=1/8, in the present notation]. Recently, we have demonstrated that the quantum collapse is suppressed and the GS is restored if repulsive interactions between particles in the quantum gas are taken into account in the mean-field approximation. This setting can be realized in a gas of dipolar molecules attracted to the central charge, with dipole-dipole interactions taken into regard as well. Here we analyze this problem for a binary gas. GSs supported by the repulsive interactions are constructed in a numerical form, as well as by means of analytical approximations for both miscible and immiscible binary systems. In particular, the Thomas-Fermi approximation is relevant if V₀ is large enough. It is found that the GS of the miscible binary gas, both balanced and imbalanced, features a weak phase transition at another critical value, ( _V0(cr))2=1/2≡4(_V0(cr))1. The transition is characterized by an analyticity-breaking change in the structure of the wave functions at small r. To illustrate the generic character of the present phenomenology, we also consider the binary system with attraction between the species (rather than repulsion) in the case when the central potential pulls a single component only.