Topological Superfluid in one-dimensional Ultracold Atomic System with Spin-Orbit Coupling

TL;DR

This paper proposes a one-dimensional ultracold atomic system with spin-orbit coupling that supports topological superfluid phases hosting Majorana fermions, with phase diagrams showing how to access these states by tuning chemical potential and spin-orbit coupling.

Contribution

It introduces a new 1D Hamiltonian supporting Majorana fermions in ultracold atoms with spin-orbit coupling, and maps phase diagrams for different symmetry cases.

Findings

Majorana fermions exist in the topological superfluid region.

Tuning chemical potential and spin-orbit coupling can reach the topological phase.

Ultracold atoms with synthetic gauge fields are a promising platform for Majorana fermions.

Abstract

We propose a one-dimensional Hamiltonian $H_{1D}$ which supports Majorana fermions when $d_{x^{2}-y^{2}}$-wave superfluid appears in the ultracold atomic system and obtain the phase-separation diagrams both for the time-reversal-invariant case and time-reversal-symmetry-breaking case. From the phase-separation diagrams, we find that the single Majorana fermions exist in the topological superfluid region, and we can reach this region by tuning the chemical potential $\mu$ and spin-orbit coupling $\alpha_{R}$. Importantly, the spin-orbit coupling has realized in ultracold atoms by the recent experimental achievement of synthetic gauge field, therefore, our one-dimensional ultra-cold atomic system described by $H_{1D}$ is a promising platform to find the mysterious Majorana fermions.