  Exchange-antisymmetric pair wavefunctions in fermionic systems can give rise
to unconventional superconductors and superfluids with non-trivial transport
properties. The realisation of these states in controllable quantum systems,
such as ultracold gases, could enable new types of quantum simulations,
topological quantum gates, and exotic few-body states. However, p-wave and
other antisymmetric interactions are weak in naturally occurring systems, and
their enhancement via Feshbach resonances in ultracold systems has been limited
by three-body loss. In this work, we create isolated pairs of spin-polarised
fermionic atoms in a multi-orbital three-dimensional optical lattice. We
spectroscopically measure elastic p-wave interaction energies of strongly
interacting pairs of atoms near a magnetic Feshbach resonance and find pair
lifetimes to be up to fifty times larger than in free space. We demonstrate
that on-site interaction strengths can be widely tuned by the magnetic field
and confinement strength but collapse onto a universal single-parameter curve
when rescaled by the harmonic energy and length scales of a single lattice
site. Since three-body processes are absent within our approach, we are able to
observe elastic unitary p-wave interactions for the first time. We take the
first steps towards coherent temporal control via Rabi oscillations between
free-atom and interacting-pair states. All experimental observations are
compared both to an exact solution for two harmonically confined atoms
interacting via a p-wave pseudopotential, and to numerical solutions using an
ab-initio interaction potential. The understanding and control of on-site
p-wave interactions provides a necessary component for the assembly of
multi-orbital lattice models, and a starting point for investigations of how to
protect such a system from three-body recombination even in the presence of
tunnelling.
