  Topological excitations are found throughout nature, in proteins and DNA, as
dislocations in crystals, as vortices and solitons in superfluids and
superconductors, and generally in the wake of symmetry-breaking phase
transitions. In fermionic systems, topological defects may provide bound states
for fermions that often play a crucial role for the system's transport
properties. Famous examples are Andreev bound states inside vortex cores,
fractionally charged solitons in relativistic quantum field theory, and the
spinless charged solitons responsible for the high conductivity of polymers.
However, the free motion of topological defects in electronic systems is
hindered by pinning at impurities. Here we create long-lived solitons in a
strongly interacting fermionic superfluid by imprinting a phase step into the
superfluid wavefunction, and directly observe their oscillatory motion in the
trapped superfluid. As the interactions are tuned from the regime of
Bose-Einstein condensation (BEC) of tightly bound molecules towards the
Bardeen-Cooper-Schrieffer (BCS) limit of long-range Cooper pairs, the effective
mass of the solitons increases dramatically to more than 200 times their bare
mass. This signals their filling with Andreev states and strong quantum
fluctuations. For the unitary Fermi gas, the mass enhancement is more than
fifty times larger than expectations from mean-field Bogoliubov-de Gennes
theory. Our work paves the way towards the experimental study and control of
Andreev bound states in ultracold atomic gases. In the presence of spin
imbalance, the solitons created here represent one limit of the long
sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of mobile Cooper
pairs.
