## (a) Scheme of the electronic states used for creating spin-dependent optical lattices with a *J* → *J*' = *J* − 1 optical transition

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**Figure 10.** (a) Scheme of the electronic states used for creating spin-dependent optical lattices with a *J* → *J*' = *J* − 1 optical transition. (b) Lattice potential along *x* obtained by interfering a standing wave along *z* with a plane wave along *x*. The required spin-dependent lattice configuration is achieved for specific choices of polarization. (c) Geometry of the complete laser configuration generating the optical lattice potential and the laser-induced tunnelling in the *x* lattice.

**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.