## (a) Spectrum of Bogoliubov excitations (red dots) calculated for *J*_{z} = 0.2 δ and *J* = Δ^{(2)}, and compared with the prediction of Kitaev's model with *J* = Δ = Δ^{(2)} (black dots)

_{z}

**Figure 3.** (a) Spectrum of Bogoliubov excitations (red dots) calculated for *J _{z}* = 0.2 δ and

*J*= Δ

^{(2)}, and compared with the prediction of Kitaev's model with

*J*= Δ = Δ

^{(2)}(black dots). (b) Density distribution along

*x*of a zero-energy Majorana state, in planes

*A*(red line) and

*B*(blue line), revealing the non-local character of Majorana states. In the perturbative regime

*J*δ, the population in

*B*remains small.

**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.