Tightly self-trapped modes and vortices in three-dimensional bosonic condensates with electromagnetically induced gravity.

Abstract

The 1/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 tightly self-trapped 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.