  We calculate exclusive vector meson photoproduction within the Color Glass
Condensate framework in high-energy photon-nucleus scattering probed
experimentally in ultra peripheral heavy ion collisions at RHIC and at the LHC.
When the free parameters are constrained by the $\gamma+p$ data from HERA, we
predict significant nuclear suppression for both the coherent and incoherent
photoproduction cross section in the TeV range. Our results indicate that the
LHC data prefers even stronger saturation effects at the highest collision
energies. Furthermore, we demonstrate how the linear polarization of photons in
ulra peripheral collisions generates azimuthal modulations in the decay
products of the exclusively produced vector meson. We show how these
measurements can probe details of the nuclear geometry, specifically the
deformed structure of the uranium nuclei.
