(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)

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.