  Realizing strong nonlinear optical responses is a long-standing goal of both
fundamental and technological importance. Recently significant efforts have
focused on exploring excitons in solids as a pathway to achieving
nonlinearities even down to few-photon levels. However, a crucial tradeoff
arises as strong light-matter interactions require large oscillator strength
and short radiative lifetime of the excitons, which limits their interaction
strength and nonlinearity. Here we experimentally demonstrate strong nonlinear
optical responses by exploiting the coupling between excitons and carriers in
an atomically thin semiconductor of trilayer tungsten diselenide. By
controlling the electric field and electrostatic doping of the trilayer, we
observe the hybridization between intralayer and interlayer excitons along with
the formation of Fermi polarons due to the interactions between excitons and
free carriers. We find substantial optical nonlinearity can be achieved under
both continuous wave and pulsed laser excitation, where the resonance of the
hole-doped Fermi polaron blueshifts by as much as ~10 meV. Intriguingly, we
observe a remarkable asymmetry in the optical nonlinearity between electron and
hole doping, which is tunable by the applied electric field. We attribute these
features to the strong interactions between excitons and free charges with
optically induced valley polarization. Our results establish that atomically
thin heterostructures are a highly versatile platform for engineering nonlinear
optical response with applications to classical and quantum optoelectronics,
and open avenues for exploring many-body physics in hybrid Fermionic-Bosonic
systems.
