  In the presence of symmetries, one-dimensional quantum systems can exhibit
topological order, which in many cases can be characterized by a quantized
value of the many-body geometric Zak or Berry phase. We establish that this
topological Zak phase is directly related to the Zak phase of an elementary
quasiparticle excitation in the system. By considering various systems, we
establish this connection for a number of different interacting phases
including: the Su-Schrieffer-Heeger model, p-wave topological superconductors,
and the Haldane chain. Crucially, in contrast to the bulk many-body Zak phase
associated with the ground state of such systems, the topological invariant
associated with quasiparticle excitations (above this ground-state) exhibit a
more natural route for direct experimental detection. To this end, we build
upon recent work [Nature Communications 7, 11994 (2016)] and demonstrate that
mobile quantum impurities can be used, in combination with Ramsey
interferometry and Bloch oscillations, to directly measure these quasiparticle
topological invariants. Finally, a concrete experimental realization of our
protocol for dimerized Mott insulators in ultracold atomic systems is discussed
and analyzed.
