  The potential for low-threshold optical nonlinearity has received significant
attention in the fields of photonics and conceptual optical neuron networks.
Excitons in two-dimensional (2D) semiconductors are particularly promising in
this regard as reduced screening and dimensional confinement foster their
pronounced many-body interactions towards nonlinearity. However, experimental
determination of the interactions remains ambiguous, as optical pumping in
general creates a mixture of excitons and unbound carriers, where the impacts
of band gap renormalization and carrier screening on exciton energy counteract
each other. Here by comparing the influences on exciton ground and excited
states energies in the photoluminescence spectroscopy of monolayer MoSe$_2$, we
are able to identify separately the screening of Coulomb binding by the neutral
excitons and by charge carriers. The energy difference between exciton ground
state (A-1s) and excited state (A-2s) red-shifts by 5.5 meV when the neutral
exciton density increases from 0 to $4\times 10^{11}$ cm$^{-2}$, in contrast to
the blue shifts with the increase of either electron or hole density. This
energy difference change is attributed to the mutual screening of Coulomb
binding of neutral excitons, from which we extract an exciton polarizability of
$\alpha_{2D}^{\rm exciton} = 2.55\times 10^{-17}$ eV(m/V)$^2$. Our finding
uncovers a new mechanism that dominates the repulsive part of many-body
interaction between neutral excitons.
