  Recent observation of quantum emitters in monolayers of hexagonal boron
nitride (h-BN) has provided a novel platform for optomechanical experiments
where the single-photon emitters can couple to the motion of freely suspended
h-BN membrane. Here, we propose a scheme where the electronic degree of freedom
of an embedded color center is coupled to the motion of the hosting h-BN
resonator via dispersive forces. We show that the coupling of membrane
vibrations to the electronic degree of freedom of the emitter can reach the
strong regime. By suitable driving of a three-level $\Lambda$-system composed
of two spin degrees of freedom in the electronic ground state as well as an
isolated excited state of the emitter a multiple electromagnetically induced
transparency spectrum becomes available. The experimental feasibility of the
efficient vibrational ground-state cooling of the membrane via quantum
interference effects in the two-color drive scheme is numerically confirmed.
More interestingly, the emission spectrum of the defect exhibits a frequency
comb with frequency spacings as small as the fundamental vibrational mode,
which finds applications in high-precision spectroscopy.
