An exactly solvable quantum-metamaterial type model

Abstract

The key difficulty in the modelling of large quantum coherent structures lies in keeping track of nonlocal, multipoint quantum correlations between their constituent parts. Here we consider a special case of such a system, a fractal quantum metamaterial interacting with electromagnetic field, and show that it can be exactly solved by using a combination of the Haar transform and the Wigner–Weyl transform. Crucially, the obtained solution indicates that propagation of the field is strongly affected by the quantum state of the metamaterial. Theoretical and experimental investigation of finite-size precursors to exactly solvable fractal quantum structures as this will help illuminate the behaviour of generic quantum coherent structures on a similar spatiotemporal scale.