Abstract:
We study the formation of a stable self-trapped spherical quantum ball in a binary Bose–Einstein
condensate (BEC) with two-body inter-species attraction and intra-species repulsion employing
the beyond-mean-field Lee–Huang–Yang and the three-body interactions. We find that either of
these interactions or a combination of them can stabilize the binary BEC quantum ball with very
similar stationary results, and for a complete description of the problem both the terms should be
considered. These interactions lead to higher-order nonlinearities, e.g. quartic and quintic,
respectively, in a nonlinear dynamical equation compared to the cubic nonlinearity of the twobody contact interaction in the mean-field Gross–Pitaevskii equation. The higher-order
nonlinearity makes the energy infinitely large at the center of the binary ball and thus avoids its
collapse. In addition to the formation of stationary binary balls, we also study a collision between
two such balls. At large velocities, the collision is found to be elastic, which turns out to be
inelastic as the velocity is lowered. We consider the numerical solution of a beyond-mean-field
model for the binary ball as well as a single-mode variational approximation to it in this stud
