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arXiv:1601.03914

Topological Superfluidity of Spin-Orbit Coupled Bilayer Fermi Gases

Liang‐Liang Wang, Wu‐Ming Liu

Published Jan 15, 2016• 0 citations
arXivHTMLPDF

Abstract

Topological superfluid, new quantum matter that possesses gapless exotic excitations known as Majorana fermions, has attracted extensive attention recently. These excitations, which can encode topological qubits, could be crucial ingredients for fault-tolerant quantum computation. However, creating and manipulating multiple Majorana fermions remain an ongoing challenge. Loading a topologically protected system in multi-layer structures would be a natural and simple way to achieve this goal. Here we investigate the system of bilayer Fermi gases with spin-orbit coupling and show that the topological condition is significantly influenced by the inter-layer tunneling, yielding two novel topological phases, which support more Majorana Fermions. We demonstrate the existence of such novel topological phases and associated multiple Majorana fermions using bilayer Fermi gases trapped inside a harmonic potential. This research pave a new way for generating multiple Majorana fermions and would be a significant step towards topological quantum computation.

DOI
10.48550/arxiv.1601.03914

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Topological superfluid, new quantum matter that possesses gapless exotic excitations known as Majorana fermions, has attracted extensive attention recently. These excitations, which can encode topological qubits, could be crucial ingredients for fault-tolerant quantum computation. However, creating and manipulating multiple Majorana fermions remain an ongoing challenge. Loading a topologically protected system in multi-layer structures would be a natural and simple way to achieve this goal. Here we investigate the system of bilayer Fermi gases with spin-orbit coupling and show that the topological condition is significantly influenced by the inter-layer tunneling, yielding two novel topological phases, which support more Majorana Fermions. We demonstrate the existence of such novel topological phases and associated multiple Majorana fermions using bilayer Fermi gases trapped inside a harmonic potential. This research pave a new way for generating multiple Majorana fermions and would be a significant step towards topological quantum computation.
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Topological superfluids are recently discovered quantum matter that hosts topologically protected gapless edge states known as Majorana fermions---exotic quantum particles that act as their own antiparticles and obey non-Abelian statistics. Their realizations are believed to lie at the heart of future technologies such as fault-tolerant quantum computation. To date, the most efficient scheme to create topological superfluids and Majorana fermions is based on the Sau-Lutchyn-Tewari-Das Sarma model with a Rashba-type spin-orbit coupling on the x-y plane and a large out-of-plane (perpendicular) Zeeman field along the z direction. Here we propose an alternative setup, where the topological superfluid phase is driven by applying an in-plane Zeeman field. This scheme offers a number of different features, notably Cooper pairings at finite center-of-mass momentum (i.e., Fulde-Ferrell pairing) and gapless excitations in the bulk. As a result, gapless topological quantum matter with an inhomogeneous pairing order parameter appears. It features unidirectional Majorana surface states at boundaries, which propagate in the same direction and connect two Weyl nodes in the bulk. We demonstrate the emergence of such exotic topological matter and the associated Majorana fermions in spin-orbit coupled atomic Fermi gases, and we determine its parameter space. The implementation of our scheme in semiconductor/superconductor heterostructures is briefly discussed.
Majorana zero modes, quasiparticles with non-Abelian statistics, have gained increasing interest for their fundamental role as building blocks in topological quantum computation. Previous studies have mainly focused on two well-separated Majorana zero modes, which could form two degenerate states serving as one nonlocal qubit for fault-tolerant quantum memory. However, creating and manipulating multiple Majorana zero modes, which could encode more qubits, remain an ongoing research topic. Here we report that multiple Majorana zero modes can exist in atomic Fermi double wires with spin-orbit coupling and perpendicular Zeeman field. This system belongs to the topological BDI class, thus all the topological superfluids are classified by integer numbers. Especially, diverse topological superfluids can be formed in a trap, where the zero energy modes can be found at the interfaces between different topological superfluids. The structure of these zero energy modes in the trap can be engineered by the trapping potential as well as other system parameters. This system would be a significant step towards utilization of Majorana zero modes in quantum computation.
We theoretically investigate a three-dimensional Fermi gas with Rashba spin–orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde–Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space (i.e., massless Dirac fermions). The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin–orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin–orbit coupling is also studied.
The experimental realizations of spin-orbit coupling (SOC) in cold atom gases put topological superfluids (TSs) under the spotlight. The topological protection of suggested superfluid models comes from the local antiunitary symmetries of ten Altland-Zirnbauer symmetry classes. In this paper we theoretically study a two-dimensional BDI model describing spin-orbit-coupled bilayer fermionic gases with sss-wave interaction to realize mirror-symmetry- (nonlocal and unitary) protected gapped TS, beyond the paradigms suggested before. This gapped phase not only shows linearly dispersive Majorana zero modes on mirror invariant one-dimensional boundaries, but also shows Majorana corner states to realize the second-order TS (TS2) with sss-wave pairing, which is explicitly different from the nonconventional pairings in the suggested systems to realize TS2. Generally, engineering the single-particle band structures should be easier than directly engineering the complicated pairings. Considering the tremendous progress in manipulating cold atom systems, our work provides a possible route (by engineering the single-particle physics, such as SOC) to realize mirror-symmetry-protected gapped TS and TS2 in cold fermionic systems in the future.
Spin-triplet p-wave superfluids of single-species (or spin-polarized) fermionic atoms is a topological superfluid. In 2D such a superfluid supports zero-energy topological Majorana fermion excitations in order parameter defects such as vortices and sample edges. In 3D these superfluids support topologically protected Dirac points in the bulk spectrum and flat surface Majorana arcs. Despite the promise, creating a spin-triplet p-wave single-species fermionic superfluid either from direct p-wave Feshbach resonance or indirectly from the recently proposed artificial spin-orbit and Zeeman couplings can be technologically challenging. Here we show that such topological superfluids can be far more simply created by using the Kohn-Luttinger effect applied to two species of spin-polarized fermions with a density imbalance. We discuss how the topological Majorana excitations of the resulting superfluids can be identified using recently-developed experimental techniques.