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

TL;DR

This paper investigates stable, tightly-bound solitons and vortices in three-dimensional Bose-Einstein condensates with long-range $1/r$ interactions induced by laser illumination, revealing new self-trapped modes and their interactions.

Contribution

It introduces the concept of tightly self-trapped modes (TSTMs) with vorticity in 3D BECs under electromagnetically-induced gravity, including their stability and interaction dynamics.

Findings

Stable vortex TSTMs with winding numbers up to 6.

Formation of stable bound states from vortex pairs.

Inelastic collisions leading to merger or vortex formation.

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 \textit{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.