Optical Indistinguishability via Twinning Fields

Here we introduce the concept of the twinning field -- a driving electromagnetic pulse that induces an identical optical response from two distinct materials. We show that for a large class of pairs of generic many-body systems, a twinning field which renders the systems \emph{optically indistinguishable} exists. The conditions under which this field exists are derived, and this analysis is supplemented by numerical calculations of twinning fields for both the 1D Fermi-Hubbard model, and tight-binding models of graphene and hexagonal Boron Nitride. The existence of twinning fields may lead to new research directions in non-linear optics, materials science, and quantum technologies.