  We study a hybrid nano-mechanical system coupled to a spin ensemble as a
quantum simulator to favor a quantum interference effect, the
electromagnetically induced transparency (EIT). This system consists of two
nano-mechanical resonators (NAMRs), each of which coupled to a nuclear spin
ensemble. It could 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 EIT effect under the driving of a
probe microwave field. The double-EIT phenomenon emerges in the large $N$ (the
number of the nuclei) limit with 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.
