  The three-body problem, from the chaotic motions of celestial bodies to
complex microscopic particle interactions, has always been one of the most
foundational yet intricate challenges in physics since its establishment. A key
breakthrough in this domain is the Efimov effect, which represents a
significant stride in what is now known as Efimov physics. Our study uncovers a
macroscopic Efimov effect in a three-component Bose-Einstein Condensate (BEC)
system. Through theoretical analysis and numerical simulation, it is verified
that under certain conditions, three vortices form a bound state, while
removing one vortex causes the others to unbind, demonstrating topological
characteristics similar to the Borromean rings, hence termed the `vortex Efimov
effect', signifying a novel topological phase transition. We propose several
experimental approaches to realize this macroscopic Efimov effect, paving new
paths not only in many-body physics but also in exploring quantum phase
transitions and applications in quantum information.
