  Unveiling the true nature of Dark Matter (DM), which manifests itself only
through gravity, is one of the principal quests in physics. Leading candidates
for DM are weakly interacting massive particles (WIMPs) or ultralight bosons
(axions), at opposite extremes in mass scales, that have been postulated by
competing theories to solve deficiencies in the Standard Model of particle
physics. Whereas DM WIMPs behave like discrete particles ($\varrho$DM), quantum
interference between DM axions is manifested as waves ($\psi$DM). Here, we show
that gravitational lensing leaves signatures in multiply-lensed images of
background galaxies that reveal whether the foreground lensing galaxy inhabits
a $\varrho$DM or $\psi$DM halo. Whereas $\varrho$DM lens models leave well
documented anomalies between the predicted and observed brightnesses and
positions of multiply-lensed images, $\psi$DM lens models correctly predict the
level of anomalies left over by $\varrho$DM lens models. More challengingly,
when subjected to a battery of tests for reproducing the quadruply-lensed
triplet images in the system HS 0810+2554, $\psi$DM is able to reproduce all
aspects of this system whereas $\varrho$DM often fails. The ability of $\psi$DM
to resolve lensing anomalies even in demanding cases like HS 0810+2554,
together with its success in reproducing other astrophysical observations, tilt
the balance toward new physics invoking axions.
