Mechanical coupling of polar topologies and oxygen octahedra rotations in PbTiO$_3$/SrTiO$_3$ superlattices

PbTiO$_3$/SrTiO$_3$ artificial superlattices recently emerged as a prototypical platform for the emergence and study of polar topologies. While previous studies mainly focused on the polar textures inherent to the ferroelectric PbTiO$_3$ layers, the oxygen octahedra rotations inherent to the paraelectric SrTiO$_3$ layers have attracted much little attention. Here, we highlight a biunivocal relationship between distinct polar topologies -- including $a_1/a_2$ domains, polar vortices, and skyrmions -- within the PbTiO$_3$ layers and specific patterns of oxygen octahedra rotations in the SrTiO$_3$ layers. This relationship arises from a strain-mediated coupling between the two materials and is shown to be reciprocal. Through second-principles atomistic simulations, we demonstrate that each polar texture imposes a corresponding rotation pattern, while conversely, a frozen oxygen octahedra rotation dictates the emergence of the associated polar state. This confirms the strong coupling between oxygen octahedra rotations in SrTiO$_3$ and polarization in PbTiO$_3$, highlighting their cooperative role in stabilizing complex polar textures in related superlattices.