(a) Spectrum of Bogoliubov excitations (red dots) for a homogeneous system with sharp boundaries, calculated for <em>J<sub>z</sub></em> = δ and <em>J</em> = 2 Δ<sup>(2)</sup>

2013-06-24T00:00:00Z (GMT)
<p><strong>Figure 4.</strong> (a) Spectrum of Bogoliubov excitations (red dots) for a homogeneous system with sharp boundaries, calculated for <em>J<sub>z</sub></em> = δ and <em>J</em> = 2 Δ<sup>(2)</sup>. It exhibits a bulk gap Δ<sub>bulk</sub> = 0.18 <em>E<sub>r</sub></em> and a pair of zero-energy Majorana states with a residual splitting Δ<sub><em>s</em></sub> ~ 10<sup>−12</sup> <em>E<sub>r</sub></em>. (b) Evolution of the bulk gap amplitude Δ<sub>bulk</sub> as a function of the ratio <em>J<sub>z</sub></em>/δ (red line), for <em>J</em> = Δ<sup>(2)</sup>, with Δ<sup>(2)</sup> given by equation (<a href="http://iopscience.iop.org/0953-4075/46/13/134005/article#jpb448206eqn20" target="_blank">20</a>). The black line represents the prediction of second-order perturbation theory Δ<sub>bulk</sub> = 2 Δ<sup>(2)</sup>. (c) Density distribution along <em>x</em> of a zero-energy Majorana state, in planes <em>A</em> (red line) and <em>B</em> (blue line, offset for clarity). In the strong coupling regime <em>J</em> ~ δ, the population in <em>B</em> is not negligible. (d) Total density distribution along <em>x</em> calculated at zero temperature. Majorana states are not visible in this almost uniform density profile.</p> <p><strong>Abstract</strong></p> <p>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.</p>