  A single-particle mobility edge (SPME) marks a critical energy separating
extended from localized states in a quantum system. In one-dimensional systems
with uncorrelated disorder, a SPME cannot exist, since all single-particle
states localize for arbitrarily weak disorder strengths. However, if
correlations are present in the disorder potential, the localization transition
can occur at a finite disorder strength and SPMEs become possible. In this
work, we find experimental evidence for the existence of such a SPME in a
one-dimensional quasi-periodic optical lattice. Specifically, we find a regime
where extended and localized single-particle states coexist, in good agreement
with theoretical simulations, which predict a SPME in this regime.
