  Single photon emitters in atomically-thin semiconductors can be
deterministically positioned using strain induced by underlying
nano-structures. Here, we couple monolayer WSe$_2$ to high-refractive-index
gallium phosphide dielectric nano-antennas providing both optical enhancement
and monolayer deformation. For single photon emitters formed on such
nano-antennas, we find very low (femto-Joule) saturation pulse energies and up
to 10$^4$ times brighter photoluminescence than in WSe$_2$ placed on
low-refractive-index SiO$_2$ pillars. We show that the key to these
observations is the increase on average by a factor of 5 in the quantum
efficiency of the emitters coupled to the nano-antennas. This further allowed
us to gain new insights into their photoluminescence dynamics, revealing the
roles of the dark exciton reservoir and Auger processes. We also find that the
coherence time of such emitters is limited by intrinsic dephasing processes.
Our work establishes dielectric nano-antennas as a platform for high-efficiency
quantum light generation in monolayer semiconductors.
