FIG. 4. Preservation of phase coherence during transduction.

(A) Interference patterns taken at different values of n_coh. The solid curves are sinusoidal fits to the data, from which we extract the visibility. (B) Visibility as a function of the coherent phonon occupation in the mechanical resonator. The error in the visibility for the lower values of n_coh are smaller than the data point size. The data is overlaid with the expected visibility from the coherent and noise contributions $\sqrt{n_{\text{coh}}/\left(n_{\text{coh}}+n_{\text{noise}}\right)}$. The solid line considers thermal noise only (n_noise = n_th), while the dashed line also takes any other sources into account (n_noise = n_th + n_other), while both are scaled by the maximum available visibility in our setup.