  Interacting many-body systems combining confined and extended dimensions,
such as ladders and few layer systems are characterized by enhanced quantum
fluctuations, which often result in interesting collective properties. Recently
two-dimensional bilayer systems, such as twisted bilayer graphene or ultracold
atoms, have sparked a lot of interest because they can host rich phase
diagrams, including unconventional superconductivity. Here we present a
theoretical proposal for realizing high temperature pairing of fermions in a
class of bilayer Hubbard models. We introduce a general, highly efficient
pairing mechanism for mobile dopants in antiferromagnetic Mott insulators,
which leads to binding energies proportional to $t^{1/3}$, where $t$ is the
hopping amplitude of the charge carriers. The pairing is caused by the energy
that one charge gains when retracing a string of frustrated bonds created by
another charge. Concretely, we show that this mechanism leads to the formation
of highly mobile, but tightly bound pairs in the case of mixed-dimensional
Fermi-Hubbard bilayer systems. This setting is closely related to the
Fermi-Hubbard model believed to capture the physics of copper oxides, and can
be realized by currently available ultracold atom experiments.
