We consider the ground state of a single spin-down impurity atom interacting attractively with a spin-polarized atomic Fermi gas.
By constructing variational wave functions for polarons, molecules
and trimers, we perform a detailed study of the quantum phase
transitions between each of these bound states as a function of mass
ratio $r=m_\uparrow/m_\downarrow$ and interaction strength. We find
that Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing is mostly
superceded by the formation of a $p$-wave trimer, which can be
viewed as a FFLO molecule that has bound an additional majority
atom. For sufficiently large $r$, we find that these
transitions lie outside the region of superfluid-normal phase
separation in spin-imbalanced Fermi gases and should thus be
observable in experiment, unlike the well-studied equal-mass case.