Tightly bound solitons and vortices in three-dimensional bosonic condensates with the electromagnetically-induced gravity

The $1\mathrm{/}r$ long-range interaction, induced by laser illumination, offers a mechanism for the implementation of stable self-trapping in Bose-Einstein condensates (BECs) in the three-dimensional free space. Using the variational approximation and numerical solutions, we find that self-trapped states in this setting , with attractive nonlocal and repulsive local interactions, resemble tightly-bound compactons. However, these are not true compactons but rather $\mathit{\text{tightly}}\mathit{\text{self-trapped}}\mathit{\text{modes}}$ (TSTMs), with small-amplitude nonvanishing tails. The structure of the self-trapped states is explained by an analytical solution for their tails. Further, we demonstrate that stable % TSTMs with embedded vorticity, exist in the same setting, with winding numbers up to $S=6$ (at least). Addressing two-TSTM interactions, we find that pairs of ground states (GSs, with $S=0$), as well as vortex-vortex and vortex-antivortex pairs (with $S_1=S_2$ and $S_1=-S_2$, respectively), form stably rotating bound states. Head-on collisions between vortex TSTMs, set in slow motion by kicks, are inelastic, resulting in their merger into a GS soliton, that may either remain at the collision position or move aside, shedding the angular momentum with emitted radiation, or, alternatively, lead to the formation of a vortex that also moves aside.