%0 DATA
%A Sylvain, Nascimbène
%D 2013
%T (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)
%U https://iop.figshare.com/articles/_a_Spectrum_of_Bogoliubov_excitations_red_dots_calculated_for_em_J_sub_z_sub_em_0_2_and_em_J_em_sup_/1012014
%R 10.6084/m9.figshare.1012014.v1
%2 https://iop.figshare.com/ndownloader/files/1479839
%K latter acts
%K Majorana edge state
%K topological superfluidity
%K Majorana fermions
%K Majorana states
%K 1 D gas
%K ultracold fermionic atoms
%K Feshbach molecules
%K topological superfluid
%K perturbative limit
%K 1 D system
%K Cooper pair reservoir
%K superfluid gap
%K topological superfluid boundaries
%K 2 D
%K topological superfluid phase
%K Density distribution
%K fermionic atoms
%K Bogoliubov excitations
%K uniform gas
%K 1 D tube
%X **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.