(a) Spectrum of Bogoliubov excitations (red dots) for a harmonically trapped system, calculated for Jz = 1.5 δ, J = 2 Δ(2), ω = 2π × 200 Hz
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Figure 5. (a) Spectrum of Bogoliubov excitations (red dots) for a harmonically trapped system, calculated for Jz = 1.5 δ, J = 2 Δ(2), ω = 2π × 200 Hz. It exhibits a bulk gap Δbulk = 0.22 Er and a pair of zero-energy Majorana states with a residual splitting Δs ~ 10−10 Er. (b) Evolution of the energy splitting Δs between Majorana states (red dots) and of the bulk gap Δbulk (orange dots) as a function of the trapping frequency ω. While the bulk gap essentially does not depend on ω, the splitting between Majorana states strongly decreases when decreasing the ω value, i.e. increasing the separation between Majorana fermions. (c) Density distribution along x of a zero-energy Majorana state, in planes A (red line) and B (blue line). (d) Total density distribution along x calculated at zero temperature.
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.