  Using synthetic lattices of laser-coupled atomic momentum modes, we
experimentally realize a recently proposed family of nearest-neighbor
tight-binding models having quasiperiodic site energy modulation that host an
exact mobility edge protected by a duality symmetry. These one-dimensional
tight-binding models can be viewed as a generalization of the well-known
Aubry-Andr\'{e} (AA) model, with an energy-dependent self duality condition
that constitutes an analytical mobility edge relation. By adiabatically
preparing the lowest and highest energy eigenstates of this model system and
performing microscopic measurements of their participation ratio, we track the
evolution of the mobility edge as the energy-dependent density of states is
modified by the model's tuning parameter. Our results show strong deviations
from single-particle predictions, consistent with attractive interactions
causing both enhanced localization of the lowest energy state due to
self-trapping and inhibited localization of the highest energy state due to
screening. This study paves the way for quantitative studies of interaction
effects on self duality induced mobility edges.
