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Laser induced shift of atomic states due to the AC-Stark effect has played acentral role in cold-atom physics and facilitated their emergence as analogquantum simulators. Here, we explore this phenomena in an atomically thin layerof semiconductor MoSe$_2$, which we embedded in a heterostructure enablingcharge tunability. Shining an intense pump laser with a small detuning from thematerial resonances, we generate a large population of virtual collectiveexcitations, and achieve a regime where interactions with this backgroundpopulation is the leading contribution to the AC-Stark shift. Using thistechnique we study how itinerant charges modify -- and dramatically enhance --the interactions between optical excitations. In particular, our experimentsshow that the interaction between attractive polarons could be more than anorder of magnitude stronger than those between bare excitons.

Interaction induced AC-Stark shift of exciton-polaron resonances