Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes

For over twenty years, ultra-cold atomic systems have formed an almost perfect arena for simulating different quantum many-body phenomena and exposing their non-obvious and very often counterintuitive features. Thanks to extremely precise controllability of different parameters they are able to capture different quantum properties which were previously recognized only as theoretical curiosities. Here, we go over the current experimental progress in exploring the curious one-dimensional quantum world of fermions from the perspective of three subjectively selected trends being currently under vigorous experimental validation: (i) unconventional pairing in attractively interacting fermionic mixtures, (ii) fermionic systems subjected to the artificial spin-orbit coupling, (iii) fermionic gases of atoms with high SU(N) symmetry of internal states.