Nanohertz Pendulum toward Macroscopic Entanglement under Structural Damping

Abstract

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 $G_{\mathrm{req}}=1.49$. To overcome this structural-noise penalty, we realize a $7$-mg pendulum suspended by a stepped fused-silica fiber, with an energy-decay rate $\hat{I}“/2\ddot{I}€=361(39)$ nHz ($Q\equiv \ddot{I}{‰}_0/\hat{I}“=7.3(8)\times 10^6$) at $\ddot{I}{‰}_0/2\ddot{I}€=2.63$ Hz. The reduction in $\ddot{I}{‰}_0\hat{I}“$ yields a measured gain $G_q\simeq 2.5$ relative to the previous monolithic device, exceeding the requirement.