Topology by Dissipation in Atomic Quantum Wires

TL;DR

This paper demonstrates that topological phases, including Majorana edge states and non-Abelian braiding, can emerge in open quantum systems with engineered dissipation, extending topological protection beyond Hamiltonian systems.

Contribution

It introduces a dissipative approach to realizing topological phases and Majorana modes in atomic quantum wires, highlighting the role of engineered dissipation in topological protection.

Findings

Existence of Majorana edge modes in dissipative quantum wires

Dissipative non-Abelian braiding operations demonstrated

Topological protection via a nontrivial winding number of the density matrix

Abstract

Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as "topologically protected" quantum memory and computing. While so far topological phases have been exclusively discussed in a Hamiltonian context, we show that such phases and the associated topological protection and phenomena also emerge in open quantum systems with engineered dissipation. The specific system studied here is a quantum wire of spinless atomic fermions in an optical lattice coupled to a bath. The key feature of the dissipative dynamics described by a Lindblad master equation is the existence of Majorana edge modes, representing a non-local decoherence free subspace. The isolation of the edge states is enforced by a dissipative gap in the p-wave paired bulk of the wire. We describe dissipative non-Abelian braiding operations within the Majorana subspace, and we illustrate the insensitivity to imperfections. Topological protection is granted by a nontrivial winding number of the system density matrix.