Topological Schr\"odinger cats: Non-local quantum superpositions of topological defects

TL;DR

This paper demonstrates how topological defects, such as domain walls, can be placed in quantum superpositions, creating non-local Schrödinger cat states, and explores their coherence properties and decoherence effects.

Contribution

It introduces a method to put topological defects in non-local superpositions within a quantum phase transition model, and proposes an experimental setup to observe such superpositions.

Findings

Topological defects can be coherently superposed in a quantum system.

Decoherence suppresses observable coherence in topological Schrödinger cats.

Environment interactions influence symmetry breaking and defect superpositions.

Abstract

Topological defects (such as monopoles, vortex lines, or domain walls) mark locations where disparate choices of a broken symmetry vacuum elsewhere in the system lead to irreconcilable differences. They are energetically costly (the energy density in their core reaches that of the prior symmetric vacuum) but topologically stable (the whole manifold would have to be rearranged to get rid of the defect). We show how, in a paradigmatic model of a quantum phase transition, a topological defect can be put in a non-local superposition, so that - in a region large compared to the size of its core - the order parameter of the system is "undecided" by being in a quantum superposition of conflicting choices of the broken symmetry. We demonstrate how to exhibit such a "Schr\"odinger kink" by devising a version of a double-slit experiment suitable for topological defects. Coherence detectable in such experiments will be suppressed as a consequence of interaction with the environment. We analyze environment-induced decoherence and discuss its role in symmetry breaking.