  Recent experimental advances in atomically thin transition metal
dichalcogenide (TMD) metals have unveiled a range of interesting phenomena
including the coexistence of charge-density-wave (CDW) order and
superconductivity down to the monolayer limit. The atomic thickness of
two-dimensional (2D) TMD metals also opens up the possibility for control of
these electronic phase transitions by electrostatic gating. Here we demonstrate
reversible tuning of superconductivity and CDW order in model 2D TMD metal
NbSe$_2$ by an ionic liquid gate. A variation up to ~ 50% in the
superconducting transition temperature has been observed, accompanied by a
correlated evolution of the CDW order. We find that the doping dependence of
the superconducting and CDW phase transition in 2D NbSe$_2$ can be understood
by a varying electron-phonon coupling strength induced by the gate-modulated
carrier density and the electronic density of states near the Fermi surface.
