Fractionalized Majorana modes in ultracold bosonic systems*

Fractionalized Majorana fermions, also known as parafermions, are exotic topologically protected modes that go beyond the simplest non-Abelian anyons, Majorana fermions. They commute up to a nontrivial phase factor in contrast to the minus sign for fermions. These modes are proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. With 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 two Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trench and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes.