Emulating Majorana fermions and their braiding by Ising spin chains
Emulating Majorana fermions and their braiding by Ising spin chains
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DOI：
10.1103/physrevb.96.195402
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发表时间：
2017-11-01
影响因子：
3.7
通讯作者：
Schoen, Gerd
中科院分区：
文献类型：
--
作者：
Backens, Stefan;Shnirman, Alexander;Schoen, Gerd
我们通过将费米子系统映射到伊辛自旋链上来分析马约拉纳零能态的控制。尽管伊辛系统失去了拓扑保护，但映射提供了对量子态本质的额外洞察。通过控制局域磁场，可以将伊辛链分为铁磁相和顺磁相，对应于费米子系统的拓扑部分和非拓扑部分。在本文中，我们提出了（拓扑非保护的）协议来执行编织操作，实际上还有更一般的旋转。我们首先考虑t结几何，但我们也提出了一个纯一维（1D）系统的协议。这两种装置都依赖于一个额外的自旋- 12耦合器。通过在t结几何中加入额外的自旋，我们克服了Jordan-Wigner变换的一维特性所带来的限制。在一维几何结构中，一旦链条的铁磁（拓扑）部分被移远，控制其中一个伊辛链的耦合器就应该被操纵。我们还提出了我们的方案的实验实现。一种是基于通量量子比特链，它允许所有需要的控制场。我们还描述了如何将我们的方案转化为一条超导导线链，每条导线都承载一对马约拉纳边缘态。
We analyze the control of Majorana zero-energy states by mapping the fermionic system onto a chain of Ising spins. Although the topological protection is lost for the Ising system, the mapping provides additional insight into the nature of the quantum states. By controlling the local magnetic field, one can separate the Ising chain into ferromagnetic and paramagnetic phases, corresponding to topological and nontopological sections of the fermionic system. In this paper we propose (topologically nonprotected) protocols performing the braiding operation, and in fact also more general rotations. We first consider a T-junction geometry, but we also propose a protocol for a purely one-dimensional (1D) system. Both setups rely on an extra spin-1 2 coupler. By including the extra spin in the T-junction geometry, we overcome limitations due to the 1D character of the Jordan-Wigner transformation. In the 1D geometry the coupler, which controls one of the Ising links, should be manipulated once the ferromagnetic (topological) section of the chain is moved far away. We also propose experimental implementations of our scheme. One is based on a chain of flux qubits which allows for all needed control fields. We also describe how to translate our scheme for the 1D setup to a chain of superconducting wires hosting each a pair of Majorana edge states.