Interaction induced AC-Stark shift of exciton-polaron resonances

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