Topological States in a One-Dimensional Fermi Gas with Attractive Interactions

Abstract

We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons, are doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero field.

9 pages, 4 figures including supplementary material

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• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
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• Boundary-Induced Topological and Mid-Gap States in Charge Conserving One-Dimensional Superconductors
• Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions
• Unique Signatures of Topological Phases in Two-Dimensional THz Spectroscopy
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
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• Fusion Rules of Majorana-Kramer-Pairs in Time-Reversal-Invariant Topological Superconductors
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
• Fate of Majorana zero modes by a modified real-space-Pfaffian method and mobility edges in a one-dimensional quasiperiodic lattice
• Adiabatic preparation of a number-conserving atomic Majorana phase