  Exciton-polaritons are composite bosonic quasiparticles arising from the
strong coupling of excitonic transitions and optical modes. Exciton-polaritons
have triggered wide exploration in the past decades not only due to their rich
quantum phenomena such as superfluidity, superconductivity and quantized
vortices but also due to their potential applications for unconventional
coherent light sources and all-optical control elements. Here, we report the
observation of Bose-Einstein condensation of the upper polariton branch in a
transferrable WS$_2$ monolayer microcavity. Near the condensation threshold, we
observe a nonlinear increase in upper polariton intensity. This sharp increase
in intensity is accompanied by a decrease of the linewidth and an increase of
the upper polariton temporal coherence, all of which are hallmarks of
Bose-Einstein condensation. By simulating the quantum Boltzmann equation, we
show that the upper polariton condensation only occurs for a particular range
of particle density. We can attribute the creation of Bose condensation of the
upper polariton to the following requirements: 1) the upper polariton is more
excitonic than the lower one; 2) there is relatively more pumping in the upper
branch; and 3) the conversion time from the upper to the lower polariton branch
is long compared to the lifetime of the upper polaritons.
