Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Majorana fermions with spin-orbit coupled cold atom in one-dimensional optical lattices

Chuan-Jia Shan, W. W. Cheng, J.B. Liu, Yueli Huang, T. K. Liu

Published Feb 26, 2014• 3 citations
Publisher

Abstract

We propose an alternative experimental scheme to detect the non-Abelian statistics of the Majorana fermions (MF) with a trapped atomic bosonic gas subject to a spin-orbit coupling in 1D optical lattices. The spin-orbit coupling leads to a faithful simulation of an arbitrary tunable XY spin model, where the anisotropy of the effective spin coupling can be controlled by adjusting the optical potentials, Feshbach resonance, and spin-orbit coupling. MF are created at the ends of the optical lattice segment in topological phase. By controlling the different addressing laser beams, one can move, braid, and exchange them. We also show that the non-Abelian statistics of MF can be demonstrated through distinguishing the states before and after braiding by detecting the parity operator of collective spin states.

DOI
10.1364/josab.31.000581

Related papers

Creation, manipulation and detection of Majorana fermions with cold atoms in optical lattice

Mei, Feng, Chuan-Jia Shan, Xun‐Li Feng +5 more

We propose an experimental scheme to simulate the transverse field Ising model with cold atoms trapped in one-dimensional optical lattice. Majorana fermions are created at the ends of the optical lattice segment in topological phase. By controlling the addressing lasers, one can move, fuse and braid them. We also show that the non-Abelian braiding statistics of Majorana fermions can be demonstrated unambiguously through the construction of two braiding operations and distinguishing the resulting two output orthogonal collective spin states. A nice feature of the scheme is that the strong fluorescence provided by the collective spin state can be readily detected in experiment.

arXiv:1204.3974•Apr 18, 2012•2 citations

Proposal for observing non-Abelian statistics of Majorana-Shockley fermions in an optical lattice

Dong‐Ling Deng, Sheng-Tao Wang, Kai Sun +1 more

Besides the conventional bosons and fermions, in synthetic two-dimensional (2D) materials there could exist more exotic quasiparticles with non-Abelian statistics, meaning that the quantum states in the system will be transformed by noncommuting unitary operators when we adiabatically braid the particles one around another. Here, we propose an experimental scheme to observe non-Abelian statistics with cold atoms in a 2D optical lattice. We show that the Majorana-Schockley modes associated with line defects can be braided with non-Abelian statistics through adiabatic shift of the local potentials. We also demonstrate that the braiding operations are robust against typical experimental imperfections and the readout of topological qubits can be accomplished by local measurement of the atom number.

arXiv:1408.5653•Physical Review B•Mar 23, 2015•12 citations

One-dimensional topological chains with Majorana fermions in two-dimensional nontopological optical lattices

Lei Jiang, Chunlei Qu, Chuanwei Zhang

The recent experimental realization of one-dimensional (1D) equal Rashba-Dresselhaus spin-orbit coupling (ERD-SOC) for cold atoms provides a disorder-free and highly controllable platform for the implementation and observation of Majorana fermions (MFs), analogous to the broadly studied solid-state nanowire-superconductor heterostructures. However, the corresponding 1D chains of cold atoms possess strong quantum fluctuation, which may destroy the superfluids and MFs. In this paper, we show that such 1D topological chains with MFs may be on demand generated in a two- or three-dimensional nontopological optical lattice with 1D ERD-SOC by modifying local potentials on target locations using experimentally already implemented atomic gas microscopes or patterned (e.g., double- or triple-well) optical lattices. All ingredients in our scheme have been experimentally realized, and the combination of them may pave the way for the experimental observation of MFs in a clean system.

arXiv:1503.01810•Physical Review A•Jun 13, 2016•4 citations

Probing Non-Abelian Statistics of Majorana Fermions in Ultracold Atomic Superfluid

Shi-Liang Zhu, L.-B. Shao, Z. D. Wang +1 more

We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.

arXiv:1012.5761•Physical Review Letters•Mar 8, 2011•142 citations

Majorana fermions in quasi-one-dimensional and higher-dimensional ultracold optical lattices

Chunlei Qu, Ming Gong, Yong Xu +2 more

We study Majorana fermions (MFs) in quasi-one dimensional (quasi-1D) and higher-dimensional fermionic optical lattices with a strictly 1D spin-orbit coupling, which has already been realized in cold atom experiments. We show that when the superfluid order parameters are homogeneous and are enforced to be identical along different chains, there are multiple MFs at each end with or without an experimentally tunable in-plane Zeeman field ${V}_{y}$. For ${V}_{y}=0$ the multiple MFs are topologically protected by a chiral symmetry; however, for ${V}_{y}\ensuremath{\ne}0$ the existence of multiple MFs is related to the peculiar spectrum properties of the system despite the broken chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero-energy flat band. Furthermore, when the superfluid order parameters are solved self-consistently, the multiple MFs are usually destroyed because of the inhomogeneous order parameters of either Bardeen-Cooper-Schrieffer (${V}_{y}=0$) type or Fulde-Ferrell (${V}_{y}\ensuremath{\ne}0$) type. Our results are useful to guide the experimentalists on searching for MFs in ultracold spin-orbit coupled fermionic superfluids.

arXiv:1310.7557•Physical Review A•Aug 14, 2015•12 citations

Majorana Fermions in Equilibrium and in Driven Cold-Atom Quantum Wires

Liang Jiang, Takuya Kitagawa, Jason Alicea +7 more

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.

arXiv:1102.5367•Physical Review Letters•Jun 2, 2011•753 citations
We propose an alternative experimental scheme to detect the non-Abelian statistics of the Majorana fermions (MF) with a trapped atomic bosonic gas subject to a spin-orbit coupling in 1D optical lattices. The spin-orbit coupling leads to a faithful simulation of an arbitrary tunable XY spin model, where the anisotropy of the effective spin coupling can be controlled by adjusting the optical potentials, Feshbach resonance, and spin-orbit coupling. MF are created at the ends of the optical lattice segment in topological phase. By controlling the different addressing laser beams, one can move, braid, and exchange them. We also show that the non-Abelian statistics of MF can be demonstrated through distinguishing the states before and after braiding by detecting the parity operator of collective spin states.
We propose an experimental scheme to simulate the transverse field Ising model with cold atoms trapped in one-dimensional optical lattice. Majorana fermions are created at the ends of the optical lattice segment in topological phase. By controlling the addressing lasers, one can move, fuse and braid them. We also show that the non-Abelian braiding statistics of Majorana fermions can be demonstrated unambiguously through the construction of two braiding operations and distinguishing the resulting two output orthogonal collective spin states. A nice feature of the scheme is that the strong fluorescence provided by the collective spin state can be readily detected in experiment.
Besides the conventional bosons and fermions, in synthetic two-dimensional (2D) materials there could exist more exotic quasiparticles with non-Abelian statistics, meaning that the quantum states in the system will be transformed by noncommuting unitary operators when we adiabatically braid the particles one around another. Here, we propose an experimental scheme to observe non-Abelian statistics with cold atoms in a 2D optical lattice. We show that the Majorana-Schockley modes associated with line defects can be braided with non-Abelian statistics through adiabatic shift of the local potentials. We also demonstrate that the braiding operations are robust against typical experimental imperfections and the readout of topological qubits can be accomplished by local measurement of the atom number.
The recent experimental realization of one-dimensional (1D) equal Rashba-Dresselhaus spin-orbit coupling (ERD-SOC) for cold atoms provides a disorder-free and highly controllable platform for the implementation and observation of Majorana fermions (MFs), analogous to the broadly studied solid-state nanowire-superconductor heterostructures. However, the corresponding 1D chains of cold atoms possess strong quantum fluctuation, which may destroy the superfluids and MFs. In this paper, we show that such 1D topological chains with MFs may be on demand generated in a two- or three-dimensional nontopological optical lattice with 1D ERD-SOC by modifying local potentials on target locations using experimentally already implemented atomic gas microscopes or patterned (e.g., double- or triple-well) optical lattices. All ingredients in our scheme have been experimentally realized, and the combination of them may pave the way for the experimental observation of MFs in a clean system.
We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.
We study Majorana fermions (MFs) in quasi-one dimensional (quasi-1D) and higher-dimensional fermionic optical lattices with a strictly 1D spin-orbit coupling, which has already been realized in cold atom experiments. We show that when the superfluid order parameters are homogeneous and are enforced to be identical along different chains, there are multiple MFs at each end with or without an experimentally tunable in-plane Zeeman field Vy{V}_{y}Vy​. For Vy=0{V}_{y}=0Vy​=0 the multiple MFs are topologically protected by a chiral symmetry; however, for ${V}_{y}\ensuremath{\ne}0$ the existence of multiple MFs is related to the peculiar spectrum properties of the system despite the broken chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero-energy flat band. Furthermore, when the superfluid order parameters are solved self-consistently, the multiple MFs are usually destroyed because of the inhomogeneous order parameters of either Bardeen-Cooper-Schrieffer (Vy=0{V}_{y}=0Vy​=0) type or Fulde-Ferrell (${V}_{y}\ensuremath{\ne}0$) type. Our results are useful to guide the experimentalists on searching for MFs in ultracold spin-orbit coupled fermionic superfluids.
We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.