Parafermionic zero modes in ultracold bosonic systems

Exotic topologically protected zero modes with parafermionic statistics (also
called fractionalized Majorana modes) have been proposed to emerge in devices
fabricated from a fractional quantum Hall system and a superconductor. The
fractionalized statistics of these modes takes them an important step beyond
the simplest non-Abelian anyons, Majorana fermions. Building on recent advances
towards the realization of fractional quantum Hall states of bosonic ultracold
atoms, we propose a realization of parafermions in a system consisting of
Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall
state. We show that parafermionic zero modes emerge at the endpoints of the
trenches and give rise to a topologically protected degeneracy. We also discuss
methods for preparing and detecting these modes.