(a) Spectrum of Bogoliubov excitations (red dots) for a homogeneous system with sharp boundaries, calculated for J_z = δ and J = 2 Δ⁽²⁾

Figure 4. (a) Spectrum of Bogoliubov excitations (red dots) for a homogeneous system with sharp boundaries, calculated for J_z = δ and J = 2 Δ⁽²⁾. It exhibits a bulk gap Δ_bulk = 0.18 E_r and a pair of zero-energy Majorana states with a residual splitting Δ_s ~ 10⁻¹² E_r. (b) Evolution of the bulk gap amplitude Δ_bulk as a function of the ratio J_z/δ (red line), for J = Δ⁽²⁾, with Δ⁽²⁾ given by equation (20). The black line represents the prediction of second-order perturbation theory Δ_bulk = 2 Δ⁽²⁾. (c) Density distribution along x of a zero-energy Majorana state, in planes A (red line) and B (blue line, offset for clarity). In the strong coupling regime J ~ δ, the population in B is not negligible. (d) Total density distribution along x calculated at zero temperature. Majorana states are not visible in this almost uniform density profile.

Abstract

We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along the 1D tube and laser-induced atom tunnelling, we obtain a topological superfluid phase. In the regime of weak couplings to the molecular field and for a uniform gas, the atomic system is equivalent to Kitaev's model of a p-wave superfluid. Using a numerical calculation, we show that the topological superfluidity is robust beyond the perturbative limit and in the presence of a harmonic trap. Finally, we describe how to investigate some physical properties of the Majorana fermions located at the topological superfluid boundaries. In particular, we discuss how to prepare and detect a given Majorana edge state.