The onset of gluon saturation at CERN LHC energies and new directions using quantum tomography

Perturbative QCD predicts that the gluon density in hadrons grows with
energy, or equivalently with decreasing Bjorken-x, up to a point where
non-linear effects set in to tame this growth, a phenomenon known as gluon
saturation. Studies at HERA have shown that the gluon density grows steeply
at small x. However, some of the HERA data can equally be described by
models with and without gluon saturation. At the CERN LHC it is possible to
study photon-induced interactions at unprecedented energies. In this talk,
we will present recent results of the energy dependence of the momentum
transfer distribution of photoproduced vector mesons off protons. These
results provide the first clear indication for the onset of gluon saturation
in the proton. In addition, we will discuss theoretical predictions for
similar studies using dissociative photoproduction at CERN, RHIC and EIC
energies. Finally, we will discuss new directions to study gluon saturation
and Quark Gluon Plasma physics using novel ideas inspired from Quantum
Information. As an example, we will present the study of the energy
dependence of photoproduced dijets using Quantum Tomography.