noise (see supplement). Laser cooling achieved a best value of $N_\mathrm{add} = 34~\mathrm{photons}$ of input-referred added noise (right side of Fig. \[feedforward\]e), comparable to the best feedforward performance. Unlike feedforward operation, laser cooling does not affect the background noise.

Although feedforward and laser cooling achieve comparable noise performance in the current setup, their limitations are quite different. In the presence of technical noise that limits damping rates, the performance of laser cooling is set by $n_\mathrm{th,m} \gamma_\mathrm{m}$, where $n_\mathrm{th,m}$ is the thermal phonon occupancy of the membrane. Indeed, we have studied laser cooling in a different converter with 10 times lower mechanical dissipation but a lower conversion efficiency of $12\%$, and achieved an $N_\mathrm{add} = 13~\mathrm{photons}$ of added noise. With feedforward, on the other hand, one can always completely eliminate the effect of thermal noise at the expense of feeding forward measurement noise. Provided $\Gamma_\mathrm{e}, \Gamma_\mathrm{o} \gg \gamma_\mathrm{m}$, feedforward performance is determined solely by the measurement apparatus, rather than coupling to the thermal bath. It should be emphasized that for any low-frequency mechanical mode this is a much less stringent condition on damping rates than high cooperativity ($\Gamma_\mathrm{e}, \Gamma_\mathrm{o} \gg n_\mathrm{th,m}\gamma_\mathrm{m}$). For example, in a 4 K experiment with a 