  Strongly correlated electron systems are a cornerstone of modern physics,
being responsible for groundbreaking phenomena from superconducting magnets to
quantum computing. In most cases, correlations in electrons arise exclusively
due to Coulomb interactions. In this work, we reveal that free electrons
interacting simultaneously with a light field can become highly correlated via
mechanisms beyond Coulomb interactions. In the case of two electrons, the
resulting Pearson correlation coefficient (PCC) for the joint probability
distribution of the output electron energies is enhanced over 13 orders of
magnitude compared to that of electrons interacting with the light field in
succession (one after another). These highly correlated electrons are the
result of momentum and energy exchange between the participating electrons via
the external quantum light field. Our findings pave the way to the creation and
control of highly correlated free electrons for applications including quantum
information and ultra-fast imaging.
