Anderson localization of Cooper pairs and Majorana fermions in an ultracold atomic Fermi gas with synthetic spin-orbit coupling

Abstract

We theoretically investigate two-particle and many-particle Anderson localizations of a spin-orbit coupled ultracold atomic Fermi gas trapped in a quasi-periodic potential and subjected to an out-of-plane Zeeman field. We solve exactly the two-particle problem in a finite length system by exact diagonalization and solve approximately the many-particle problem within the mean-field Bogoliubov-de Gennes approach. At a small Zeeman field, the localization properties of the system are similar to that of a Fermi gas with conventional $s$-wave interactions. As the disorder strength increases, the two-particle binding energy increases and the fermionic superfluidity of many particles disappears above a threshold. At a large Zeeman field, where the interatomic interaction behaves effectively like a $p$-wave interaction, the binding energy decreases with increasing disorder strength and the resulting topological superfluidity shows a much more robust stability against disorder than the conventional $s$-wave superfluidity. We also analyze the localization properties of the emergent Majorana fermions in the topological phase. Our results could be experimentally examined in future cold-atom experiments, where the spin-orbit coupling can be induced artificially by using two Raman lasers, and the quasi-periodic potential can be created by using bichromatic optical lattices.

6 pages and 5 figures

References in corpus (22)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Anderson Transitions
• Theory of ultracold Fermi gases
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
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• A one-dimensional liquid of fermions with tunable spin
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• Coupling Identical 1D Many-Body Localized Systems
• Nature of the superconductor-insulator transition in disordered superconductors
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• Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
• Observation of a two-dimensional Fermi gas of atoms
• Phase fluctuations in a strongly disordered s-wave superconductor close to the metal-insulator transition
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases
• From Planar Solitons to Vortex Rings and Lines: Cascade of Solitonic Excitations in a Superfluid Fermi Gas
• Majorana fermions in one-dimensional spin-orbit coupled Fermi gases
• Soliton-induced Majorana fermions in a one-dimensional atomic topological superfluid

Cited by in corpus (10)

• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials
• Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing
• Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids
• Almost mobility edges and existence of critical regions in one-dimensional quasiperiodic lattices
• Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction
• Unconventional superfluidity of superconductivity on Penrose lattice
• Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states
• Anderson Localization in Degenerate Spin-Orbit Coupled Fermi Gases with Disorder
• Generalized Aubry-Andre-Harper Models in Optical Superlattices