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.
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