  We investigate many-body properties of equally populated three-component
fermions with attractive three-body contact interaction in one dimension. A
diagrammatic approach suggests the possible occurrence of Cooper triples at low
temperature, which are three-body counterparts of Cooper pairs with a two-body
attraction. We develop a minimal framework that bridges the crossover from
tightly-bound trimers to Cooper triples with increasing chemical potential and
show how the formation of Cooper triples occurs in the grand-canonical phase
diagram. Moreover, we argue that this non-trivial crossover is similar to the
hadron-quark crossover proposed in dense matter. A coexistence of
medium-induced triples and the underlying Fermi sea at positive chemical
potential is analogous to quarkyonic matter consisting of baryonic excitations
and the underlying quark Fermi sea. The comparison with the existing quantum
Monte Carlo results implies that the emergence of these kinds of three-body
states can be a microscopic origin of the peak of the sound velocity along the
crossover.
