  In dense atomic gases the interaction between transition dipoles and photons
leads to the formation of many-body states with collective dissipation and
long-ranged forces. Despite decades of research, a full understanding of this
paradigmatic many-body problem is still lacking. Here, we put forward and
explore a scenario in which a dense atomic gas is weakly excited by an
off-resonant laser field. We develop the theory for describing such dressed
many-body ensembles and show that collective excitations are responsible for
the emergence of many-body interactions, i.e. effective potentials that cannot
be represented as a sum of binary terms. We illustrate how interaction effects
may be probed through microwave spectroscopy via the analysis of time-dependent
line-shifts, and show that these signals are sensitive to the phase pattern of
the dressing laser. Our study offers a new perspective on dense atomic
ensembles interacting with light and promotes this platform as a setting for
the exploration of rich non-equilibrium many-body physics.
