  Topological insulators in the AIII symmetry class lack experimental
realization. Moreover, fractionalization in one-dimensional topological
insulators has not been yet directly observed. Our work might open
possibilities for both challenges. We propose a one-dimensional model realizing
the AIII symmetry class which can be realized in current experiments with
ultracold atomic gases. We further report on a distinctive property of
topological edge modes in the AIII class: in contrast to those in the well
studied BDI class, they have non-zero momentum. Exploiting this feature we
propose a path for the detection of fractionalization. A fermion added to an
AIII system splits into two halves localized at opposite momenta, which can be
detected by imaging the momentum distribution.
