Topological states in one dimensional Fermi gases without proximity coupling to a superconductor

Recently signatures of Majorana bound states, the hallmark of topological superconductivity, have been observed in nano-wires with Rashba spin-orbit coupling, a Zeeman field and proximity coupling to an external superconductor.  In this talk i will discuss the possibility of realizing topological states in an ultra-cold Fermi gas without the proximity coupling to the external superconductor, which is very hard to achieve in these systems. I will show that intrinsic attractive interactions in the gas give rise to a new type of Majorana modes. I will also discuss the experimental implications of the zero modes, which may be observed as sharp peaks in the low-frequency response at an energy which generically scales as (1/L)^(K/2) where K is the Luttinger parameter.