## (a) Energy of the Bogoliubov excitations as a function of the chemical potential μ

**Figure 8.** (a) Energy of the Bogoliubov excitations as a function of the chemical potential μ. The parameters are the same as for figure 5, expect with a trap frequency ω/2π = 600 Hz. The bulk hole sector is pictured in blue. Starting with a system prepared at low temperature in the trivial phase (μ −2 *E _{r}*), the Majorana state connected to the hole sector of the trivial superfluid (in red) can be prepared by increasing adiabatically the chemical potential up to μ = 0. (b) Expected fidelity \mathcal {F} as a function of the ramp duration

*T*(black dots). The solid line is an exponential fit to the numerical data. A fidelity \mathcal {F}>0.9 is expected for ramp durations

*T*> 3300 /

*E*120 ms.

_{r}**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.