# Topological states in one-dimensional Fermi gases with spin-orbit coupling

## Jonathan Ruhman

We show that a one dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field and intrinsic attractive interactions exhibits a novel topological superfluid state, which forms in spite of total number conservation and the absence of single particle gap. Majorana zero modes are localized to the interface between a topological region in the middle of the trap and trivial regions at it’s wings. The topological degeneracy in this state is protected by the total spin ½ parity and generally scales as (1/L)^(K/2) where L is the distance between the edge states and K is the Luttinger parameter of the charge mode. We also discuss the experimental implications of the topological order on the low energy response of the systems to external trap oscillations.