  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 pairs of generic many-body systems, a
twinning field which renders the systems \emph{optically indistinguishable}
always exists. The conditions under which this field is unique are derived, and
this analysis is supplemented by numerical calculations of twinning fields for
the Fermi-Hubbard model. The universal existence of twinning fields may lead to
new research directions in non-linear optics, materials science, and quantum
technologies.
