  Difficult problems described in terms of interacting quantum fields evolving
in real time or out of equilibrium are abound in condensed-matter and
high-energy physics. Addressing such problems via controlled experiments in
atomic, molecular, and optical physics would be a breakthrough in the field of
quantum simulations. In this work, we present a quantum-sensing protocol to
measure the generating functional of an interacting quantum field theory and,
with it, all the relevant information about its in or out of equilibrium
phenomena. Our protocol can be understood as a collective interferometric
scheme based on a generalization of the notion of Schwinger sources in quantum
field theories, which make it possible to probe the generating functional. We
show that our scheme can be realized in crystals of trapped ions acting as
analog quantum simulators of self-interacting scalar quantum field theories.
