Analog of the electromagnetically-induced-transparency effect for two nanomechanical or micromechanical resonators coupled to a spin ensemble

We study a hybrid nanomechanical system coupled to a spin ensemble as a quantum simulator to favor a quantum interference effect, electromagnetically induced transparency (EIT). This system consists of two nanomechanical resonators (NAMRs), each of which is coupled to a nuclear spin ensemble, and can be regarded as a crucial element in the quantum network of NAMR arrays coupled to spin ensembles. Here, the nuclear spin ensembles behave as a long-lived transducer to store and transfer the NAMRs' quantum information. This system shows the analog of the EIT effect under the driving of a probe microwave field. The double EIT phenomenon emerges in the large-N (the number of nuclei) limit within the low excitation approximation, because the interactions between the spin ensemble and the two NAMRs are reduced to the coupling of three harmonic oscillators. Furthermore, the group velocity is reduced in the two absorption windows.