Topology by dissipation

TL;DR

This paper demonstrates how engineered dissipation can induce and stabilize topological states in fermionic systems, providing a new approach to realize topological phases and Majorana modes through targeted cooling.

Contribution

It develops a theoretical framework for topological order driven by dissipation, including a classification scheme and analysis of edge modes in cold atom models.

Findings

Dissipation can be used as the main resource for topological state preparation.

Majorana edge modes can emerge in dissipative fermionic systems.

A symmetry-based classification of dissipative topological states is established.

Abstract

Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into a topological phase starting from an arbitrary initial state. We explore the concept of topological order in this setting, developing and applying a general theoretical framework based on the system density matrix which replaces the wave function appropriate for the discussion of Hamiltonian ground-state physics. We identify key analogies and differences to the more conventional Hamiltonian scenario. Differences mainly arise from the fact that the properties of the spectrum and of the state of the system are not as tightly related as in a Hamiltonian context. We provide a symmetry-based topological classification of bulk steady states and identify the classes that are achievable by means of quasi-local dissipative processes driving into superfluid paired states. We also explore the fate of the bulk-edge correspondence in the dissipative setting, and demonstrate the emergence of Majorana edge modes. We illustrate our findings in one- and two-dimensional models that are experimentally realistic in the context of cold atoms.