Nanohertz Pendulum toward Macroscopic Entanglement under Structural Damping

Pendulums are attractive for macroscopic quantum control because gravity dilution reduces mechanical loss, while the $1/f$ force-noise spectrum associated with structural damping allows nearly lossless trapping to suppress the thermal noise sampled at an upward-shifted resonance. The same $1/f$ spectrum, however, produces a low-frequency tail that penalizes entanglement. With $10\%$ detection loss, we find that this tail raises the required back-action-to-thermal force-noise ratio by about $50\%$, corresponding to a required suspension gain $G_{\rm req}=1.49$. To overcome this structural-noise penalty, we realize a $7$-mg pendulum suspended by a stepped fused-silica fiber, with an energy-decay rate $\Gamma/2\pi=361(39)$ nHz ($Q\equiv\omega_0/\Gamma=7.3(8)\times10^6$) at $\omega_0/2\pi=2.63$ Hz. The reduction in $\omega_0\Gamma$ yields a measured gain $G_q\simeq2.5$ relative to the previous monolithic device, exceeding the requirement.