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 MoSe2​, 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 two orders of
magnitude stronger than those between bare excitons