  Transitions metal dichalcogenides (TMDs) are direct semiconductors in the
atomic monolayer (ML) limit with fascinating optical and spin-valley
properties. The strong optical absorption of up to 20 % for a single ML is
governed by excitons, electron-hole pairs bound by Coulomb attraction. Excited
exciton states in MoSe$_2$ and MoTe$_2$ monolayers have so far been elusive due
to their low oscillator strength and strong inhomogeneous broadening. Here we
show that encapsulation in hexagonal boron nitride results in emission line
width of the A:1$s$ exciton below 1.5 meV and 3 meV in our MoSe$_2$ and
MoTe$_2$ monolayer samples, respectively. This allows us to investigate the
excited exciton states by photoluminescence upconversion spectroscopy for both
monolayer materials. The excitation laser is tuned into resonance with the
A:1$s$ transition and we observe emission of excited exciton states up to 200
meV above the laser energy. We demonstrate bias control of the efficiency of
this non-linear optical process. At the origin of upconversion our model
calculations suggest an exciton-exciton (Auger) scattering mechanism specific
to TMD MLs involving an excited conduction band thus generating high energy
excitons with small wave-vectors. The optical transitions are further
investigated by white light reflectivity, photoluminescence excitation and
resonant Raman scattering confirming their origin as excited excitonic states
in monolayer thin semiconductors.
