  We demonstrate the integration of a thin BaTiO$_3$ (BTO) membrane with
monolayer MoSe$_2$ in a dual gate device that enables in-situ manipulation of
the BTO ferroelectric polarization with a voltage pulse. While two-dimensional
(2D) transition metal dichalcogenides (TMDs) offer remarkable adaptability,
their hybrid integration with other families of functional materials beyond the
realm of 2D materials has been challenging. Released functional oxide membranes
offer a solution for 2D/3D integration via stacking. 2D TMD excitons can serve
as a local probe of the ferroelectric polarization in BTO at a heterogeneous
interface. Using photoluminescence (PL) of MoSe$_2$ excitons to optically
readout the doping level, we find that the relative population of charge
carriers in MoSe$_2$ depends sensitively on the ferroelectric polarization.
This finding points to a promising avenue for future-generations versatile
sensing devices with high sensitivity, fast read-out, and diverse applicability
for advanced signal processing.
