  We theoretically study the spectral properties of a pump-probe driven hybrid
spinning optomechanical ring resonator optically coupled with a two-level
quantum emitter (QE or qubit). Recently we have shown [arXiv:1810.03709] that
in the absence of the emitter the coupled cavity version of this setup is not
only capable of nonreciprocal light propagation but can also exhibit slow &
fast light propagation. In this work, we investigate in what ways the presence
of a single QE coupled with the optical whispering gallery modes of the
spinning optomechanical resonator can alter the probe light nonreciprocity.
Under the weak-excitation assumption and mean-field approximation, we find that
the interplay between the rotational/spinning Sagnac-effect and the qubit
coupling can lead to the enhancement both in the optomechanically induced
transparency (OMIT) peak value and in the width of the transparency window due
to the opening of qubit-assisted back reflection channel. However, compared to
the no-qubit case, we notice that such an enhancement comes at the cost of
degrading the group delay in probe light transmission by a factor of 1/2 for
clockwise rotary directions. The target applications of these results can be in
the areas of quantum circuitry and in non-reciprocal quantum communication
protocols where QEs are a key component.
