Engineering optomechanically induced transparency by coupling a qubit to a spinning resonator

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.