Spin-orbit-coupled topological Fulde-Ferrell states of fermions in a harmonic trap
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Motivated by recent experimental breakthroughs in generating spin-orbit coupling in ultracold Fermi gases using Raman laser beams, we present a systematic study of spin-orbit-coupled Fermi gases confined in a quasi-one-dimensional trap in the presence of an in-plane Zeeman field (which can be realized using a finite two-photon Raman detuning). We find that a topological Fulde-Ferrell state will emerge, featuring finite-momentum Cooper pairing and zero-energy Majorana excitations localized near the edge of the trap based on the self-consistent Bogoliubov–de Gennes (BdG) equations. We find analytically the wave functions of the Majorana modes. Finally, using the time-dependent BdG, we show how the finite-momentum pairing field manifests itself in the expansion dynamics of the atomic cloud.
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Jiang, Lei, Tiesinga, Eite, Liu, Xia-Ji, et al.. "Spin-orbit-coupled topological Fulde-Ferrell states of fermions in a harmonic trap." Physical Review A, 90, no. 5 (2014) American Physical Society: https://doi.org/10.1103/PhysRevA.90.053606.