Macroscopic Borromean and anti-Borromean states of quantized vortices

Borromean states refer to a class of bound states with special topological structures, generally thought to exist only in microscopic systems. In this paper, we investigate vortex bound states in three-component Bose-Einstein condensates using coupled Gross-Pitaevskii equations. Specifically, through the competition between two-body and three-body interactions, we identify the emergence of vortex Borromean states, where only three vortices form a stable bound state while any two-vortex subsystems remain unbound. Our theoretical analysis and numerical simulations provide a comprehensive phase diagram of the vortex Borromean states. Additionally, we uncover an unconventional topological phase---a vortex anti-Borromean state---in which two vortices bind together but separate upon the addition of a third vortex. This study highlights the complex role of three-body interactions in macroscopic systems and offers different insights into the topology and phase transitions of multicomponent vortex systems.