Non-local quantum superpositions of topological defects

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(1,2). 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). Here 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 with 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 dub such a topological Schrodinger-cat state a 'Schrodinger kink', and devise a version of a double-slit experiment suitable for topological defects to describe one possible manifestation of the phenomenon. Coherence detectable in such experiments will be suppressed as a consequence of interaction with the environment. We analyse the environment-induced decoherence and discuss its role in symmetry breaking.