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arXiv:2312.15878

Collisions of Majorana Zero Modes

Liang‐Liang Wang, Wenjun Shao, Jian Li

Published Dec 26, 2023• 0 citations
arXivHTMLPDF

Abstract

We investigate the collisions of Majorana zero modes, which are presented as inter-soliton collisional events in fermionic superfluids with spin-orbit coupling. Our results demonstrate that, the zero energy splitting, induced by the overlapping of inter-soliton Majorana wave-functions upon collision, generates an effective repulsive force for Majorana states, which in turn protected themselves against into bulk excitation. As a result, the collision between solitons associated with Majorana zero modes appears to be repulsive and elastic, as they do not penetrate each other but instead repel without energy loss. As well, similar repulsive behavior is observed in collisions between soliton-induced and defect-pinned Majorana zero modes. Our research offers new insights into the features of Majorana fermions, and robustness in the collisions of Majorana zero modes bodes well for the prospects of topological quantum computation with a multitude of Majorana qubits.

DOI
10.48550/arxiv.2312.15878

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We investigate the collisions of Majorana zero modes, which are presented as inter-soliton collisional events in fermionic superfluids with spin-orbit coupling. Our results demonstrate that, the zero energy splitting, induced by the overlapping of inter-soliton Majorana wave-functions upon collision, generates an effective repulsive force for Majorana states, which in turn protected themselves against into bulk excitation. As a result, the collision between solitons associated with Majorana zero modes appears to be repulsive and elastic, as they do not penetrate each other but instead repel without energy loss. As well, similar repulsive behavior is observed in collisions between soliton-induced and defect-pinned Majorana zero modes. Our research offers new insights into the features of Majorana fermions, and robustness in the collisions of Majorana zero modes bodes well for the prospects of topological quantum computation with a multitude of Majorana qubits.
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.
Abstract By solving the Bogoliubov–de Gennes equations analytically, we derive the fermionic zero-modes satisfying the Majorana property that exist in vortices of a two-dimensional s-wave Fermi superfluid with spin–orbit coupling and Zeeman spin-splitting. The Majorana zero-mode becomes normalisable and exponentially localised to the vicinity of the vortex core when the superfluid is topologically non-trivial. We calculate the energy splitting due to Majorana hybridisation and identify that the s-wave Majorana vortices obey non-Abelian statistics.
The ground state behavior of the spinless fermion chain with an interaction between fermions at neighboring sites is studied for free open boundaries. For the strong enough repulsion boundary gapless states (bound state of Majorana operators from opposite sites of the chain) can exist inside the gap for bulk excitations, i.e., in the topological insulator regime. We propose to use those Majorana zero modes as topological qubits, similar to the ones in one-dimensional topological superconductors. Possible physical realizations of the considered model are discussed.
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.
We investigate a fermionic superfluid with Raman-induced spin-orbit coupling immersed in a Bose-Einstein condensate. By minimizing the total free energy, we find that, with moderate repulsive interspecies interaction, a phase separation occurs where the otherwise nontopological uniform phase is divided into two parts: a purely fermionic one and a Bose-Fermi mix characterized by nontrivial topology with the winding number W=1W=1W=1. We verify that Majorana zero modes emerge at the phase interfaces by numerical simulations of the coupled Bogoliubov--de Gennes and Gross--Pitaevskii equations in real space. The tunability of the phase interfaces enables a direct manipulation of the predicted Majorana zero modes.
Abstract We explore the topological phase, which involves Majorana type topological zero mode fermions (MTZFs) at the edge, using d–wave superfluid with Rashba spin-orbit coupling (SOC) interactions. The self-Hermitian of this MTZF( γ†(k)=γ(k){{\boldsymbol{\gamma }}}^{{\boldsymbol{\dagger }}}{\boldsymbol{(}}{\bf{k}}{\boldsymbol{)}}{\boldsymbol{=}}{\boldsymbol{\gamma }}{\boldsymbol{(}}{\bf{k}}{\boldsymbol{)}}γ†(k)=γ(k) γ † ( k ) = γ ( k ) ) is similar to that of the Majorana fermions (MFs) ( γ†=γ{{\boldsymbol{\gamma }}}^{{\boldsymbol{\dagger }}}={\boldsymbol{\gamma }}γ†=γ γ † = γ ). We show that, to realize a single MTZF at each edge in superfluid with d–wave pairing in a Majorana type Kramers Doublet (MTKD) state, it is important to lift both the spin and the Dirac Cones degeneracies. These non-Abelian anyons obey the non-Abelian statistics which may be useful to realize topological quantum computation. We suggest that the topological feature could be tested experimentally in superfluids of cold fermionic atoms with laser field induced spin orbit interactions. These studies give a new possible way to investigate the MTZFs in a two-dimensional (2D) system as compared to MFs in the one-dimensional (1D) nano-wire and 2D system, and enrich the theoretical research on finding non-Abelian anyons in topological system.