  We report the first numerical observation of composite fermion (CF) states in
fractional Chern insulators (FCI) using exact diagonalization. The ruby lattice
Chern insulator model for both fermions and bosons exhibits a clear signature
of CF states at filling factors 2/5 and 3/7 (2/3 and 3/4 for bosons). The
topological properties of these states are studied through several approaches.
Quasihole and quasielectron excitations in FCI display similar features as
their fractional quantum hall (FQH) counterparts. The entanglement spectrum of
FCI groundstates shows an identical fingerprint to its FQH partner. We show
that the correspondence between FCI and FQH obeys the emergent symmetry already
established, proving the validity of this approach beyond the clustered states.
We investigate other Chern insulator models and find similar signatures of CF
states. However, some of these systems exhibit strong finite size effects.
