  Monolayer semiconductors are atomically thin quantum wells with strong
confinement of electrons in two-dimensional (2D) plane. Here, we experimentally
study the out-of-plane polarizability of excitons in hBN-encapsulated monolayer
WSe$_{2}$ in strong electric fields of up to 1.6 V/nm (16 MV/cm). We monitor
free and bound exciton photoluminescence peaks with increasing electric fields
at a constant carrier density, carefully compensating for unintentional
photodoping in our double-gated device at 4K. We show that the Stark shift is <
0.4 meV despite the large electric fields applied, yielding an upper limit of
polarizability {\alpha}$_{z}$ to be ~ 10$^{-11}$ Dm/V. Such a small
polarizability, which is nearly two orders of magnitude smaller than the
previously reported value for MoS$_{2}$, indicates strong atomic confinement of
electrons in this 2D system and highlights the unusual robustness of free
excitons against surface potential fluctuations.
