  Borromean ring refers to a peculiar structure where three rings are linked
together while any two of them are unlinked. Here we propose the realization of
its quantum mechanical analog in a many-body system of three-component
ultracold bosons. Namely, we identify the {\it Borromean droplet}, where only
the ternary bosons can form a self-bound droplet while any binary subsystems
cannot. Its formation is facilitated by an additional attractive force induced
by the density fluctuation of a third component, which enlarges the mean-field
collapse region in comparison to the binary case and renders the formation of
Borromean droplet after incorporating the repulsive force from quantum
fluctuations. Outside the Borromean regime, the competition between ternary and
binary droplets leads to an interesting phenomenon of droplet phase separation,
manifested by double plateaus in the density profile. We further show that the
transition between different droplets and gas phase can be conveniently tuned
by boson numbers and interaction strengths. The study reveals the possibility
of Borromean binding in the many-body world and sheds light on more intriguing
many-body bound state formed in multi-component systems.
