After their introduction in the context of the relativistic Dirac equation, Majorana fermions have recently experienced a renewed interest for their relevance in the description of topological superconducting models.
In this talk I will investigate the possibility of realizing zero-energy Majorana fermions in cold-atom experiments.
First, I will discuss a theory for Majorana fermions that is fully number-conserving based on ladders whose legs exchange only pairs of particles; in particular, I will present an exactly-solvable toy-model for this setup.
Second, I will show that one-dimensional Ytterbium gases offer a natural experimental playground for the experimental implementation and verification of such theory.
Finally, if time will allow, I will comment on the recent quest for exploring beyond-Majorana physics based on the concept of parafermions.
 Iemini, Mazza, Rossini, Fazio, Diehl, PRL 115 156402 (2015)
 Iemini, Mazza, Fallani, Zoller, Fazio, Dalmonte, PRL 118 200404 (2017)
 Mazza, Iemini, Dalmonte, Mora, arXiv:1801.08548 (2018)