$12~\mathrm{kHz}$, while a $100~\mathrm{kHz}$ bandwidth was achieved at $\kappa_\mathrm{o} = 2 \pi \times 3~\mathrm{MHz}$.

During the conversion process, vibrational noise is added to the signal. In order to explore correlations in this noise, we turn off the weak probe tone and return to a high-stability configuration with $\eta_\mathrm{M} = 43\%$, but smaller pump power ($\Gamma_\mathrm{e} \approx \Gamma_\mathrm{o}$, $\Gamma_\mathrm{T} = 2 \pi \times 200~\mathrm{Hz}$). In this configuration electro/optomechanical cooling of the mechanical mode is diminished, while still maintaining $\Gamma_\mathrm{e},\Gamma_\mathrm{o} \gg \gamma_\mathrm{m}$. We perform heterodyne measurements of the noise exiting both converter ports (see supplement), and analyze the results in the frequency domain: $X(\omega)$ and $Y(\omega)$ will denote respectively the real and imaginary parts of the Fourier transform of the noise time stream at detuning $+\omega$ from the pump. The total power spectral density is then $S(\omega) = \langle X^2(\omega) \rangle + \langle Y^2(\omega) \rangle$, and is reported in units of $\mathrm{photons/s/Hz}$, or more simply photons, referred to the converter output. For example, an ideal heterodyne measurement of $S( \omega )$ gives a background noise level of 1 photon, and $50\%$ loss in the measurement chain would double the background level.

The microwave real power spectral density, $\langle X_\mathrm{e}(\omega) X_\mathrm{e}(\omega) \rangle$, exhibits 