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arXiv:2608.02462

Nanohertz Pendulum toward Macroscopic Entanglement under Structural Damping

Azusa Sawada, Hina Nakano, Kanta Watanabe, Gaku Ohashi, Shota Okumura, Nobuyuki Matsumoto

quant-phphysics.ins-detSubmitted Aug 3, 2026• Announced Aug 4, 2026• 0 citations
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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 $G_{\rm req}=1.49$. To overcome this structural-noise penalty, we realize a $7$-mg pendulum suspended by a stepped fused-silica fiber, with an energy-decay rate $Γ/2π=361(39)$ nHz ($Q\equivω_0/Γ=7.3(8)\times10^6$) at $ω_0/2π=2.63$ Hz. The reduction in $ω_0Γ$ yields a measured gain $G_q\simeq2.5$ relative to the previous monolithic device, exceeding the requirement.

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Pendulums are attractive for macroscopic quantum control because gravity dilution reduces mechanical loss, while the 1/f1/f1/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/f1/f1/f spectrum, however, produces a low-frequency tail that penalizes entanglement. With 10%10\%10% detection loss, we find that this tail raises the required back-action-to-thermal force-noise ratio by about 50%50\%50%, corresponding to a required suspension gain Greq=1.49G_{\rm req}=1.49Greq​=1.49. To overcome this structural-noise penalty, we realize a 777-mg pendulum suspended by a stepped fused-silica fiber, with an energy-decay rate Γ/2π=361(39)Γ/2π=361(39)Γ/2π=361(39) nHz (Q≡ω0/Γ=7.3(8)×106Q\equivω_0/Γ=7.3(8)\times10^6Q≡ω0​/Γ=7.3(8)×106) at ω0/2π=2.63ω_0/2π=2.63ω0​/2π=2.63 Hz. The reduction in ω0Γω_0Γω0​Γ yields a measured gain Gq≃2.5G_q\simeq2.5Gq​≃2.5 relative to the previous monolithic device, exceeding the requirement.
We present the mechanical squeezing of a mg-scale suspended mirror (i.e. a pendulum) near quantum regimes through continuous linear position measurement. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity. The position uncertainty in the measured data is reduced and squeezed to 470470470 times the zero-point amplitude xzpfx_{\rm zpf}xzpf​ with a purity of about 0.0004, by means of optimal state estimation through causal Wiener filtering. The purity of the squeezed state is clearly maximized by the Wiener filter, based on precisely identified optomechanical parameters. This is the first step for measurement-based quantum control of macroscopic pendulums, e.g. generation of an entanglement state between macroscopic pendulums. Such quantum control will provide a direct insight into the quantum to classical transition and will pave the way to test semiclassical gravity and gravity sourced by macroscopic quantum oscillators.
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We present the mechanical squeezing of a mg-scale suspended mirror (i.e. a pendulum) near quantum regimes through continuous linear position measurement. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity. The position uncertainty in the measured data is reduced and squeezed to 470470470 times the zero-point amplitude xzpfx_{\rm zpf}xzpf​ with a purity of about 0.0004, by means of optimal state estimation through causal Wiener filtering. The purity of the squeezed state is clearly maximized by the Wiener filter, based on precisely identified optomechanical parameters. This is the first step for measurement-based quantum control of macroscopic pendulums, e.g. generation of an entanglement state between macroscopic pendulums. Such quantum control will provide a direct insight into the quantum to classical transition and will pave the way to test semiclassical gravity and gravity sourced by macroscopic quantum oscillators.
We present our development of a table-top quantum sensor with femtometer sensitivity within the acoustic frequency band. Our sensor utilises the expertise developed within the gravitational-wave community, particularly in the control of high-finesse, suspended interferometers, and the mitigation of seismic and thermal noise. We construct a system consisting of a cryostat-mounted four-stage suspension supporting two cavities with optical finesse in excess of 350,000. We use active isolation of the entire cryostat system to achieve an order-of-magnitude of reduction of the seismic noise prior to the passive isolation of the internal suspension. We achieve the femtometer sensitivity using a custom-made phase lock loop. With further enhancements to the readout electronics and suspension characteristics, we aim to reach the quantum radiation pressure noise. This sensor holds the potential for future applications in demonstrating macroscopic entanglement and testing semi-classical and quantum gravity theories.
The application of quantum mechanics to macroscopic motion suggests many counterintuitive phenomena. While the quantum nature of the motion of individual atoms and molecules has long been successfully studied, an equivalent demonstration of the motion of a near-macroscopic structure remains a challenge in experimental physics. A nanomechanical resonator is an excellent system for such a study. It typically contains > 10 10 atoms, and it may be modeled in terms of macroscopic parameters such as bulk density and elasticity. Yet it behaves like a simple harmonic oscillator, with mass low enough and resonant frequency high enough for its quantum zero-point motion and single energy quanta to be experimentally accessible. In pursuit of quantum phenomena in a mechanical oscillator, two important goals are to prepare the oscillator in its quantum ground state, and to measure its position with a precision limited by the Heisenberg uncertainty principle. In this work we have demonstrated techniques that advance towards both of these goals. Our system comprises a 30 micron × 170 nm, 2.2 pg, 5.57 MHz nanomechanical resonator capacitively coupled to a 5 GHz superconducting microwave resonator. The microwave resonator and nanomechanical resonator are fabricated together onto a single silicon chip and measured in a dilution refrigerator at temperatures below 150 mK. At these temperatures the coupling of the motion to the thermal environment is very small, resulting in a very high mechanical Q, approaching ∼ 10 6 . By driving with a microwave pump signal, we observed sidebands generated by the mechanical motion and used these to measure the thermal motion of the resonator. Applying a pump tone red-detuned from the microwave resonance, we used the microwave field to damp the mechanical resonator, extracting energy and "cooling" the motion in a manner similar to optical cooling of trapped atoms. Starting from a mode temperature of ∼ 150 mK, we reached ∼ 40 mK by this "backaction cooling" technique, corresponding to an occupation factor only ∼ 150 times above the ground state of motion. We also determined the precision of our device in measurement of position. Quantum mechanics dictates that, in a continuous position measurement, the precision may be no better than the zero-point motion of the resonator. Increasing the coupling of the resonator to detector will eventually result in back-action driving of the motion, adding imprecision and enforcing this limit. We demonstrated that our system is capable of precisions approaching this limit, and identified the primary experimental factors preventing us from reaching it: noise added to the measurement by our amplifier, and excess dissipation appearing in our microwave resonator at high pump powers. Furthermore, by applying both red- and blue-detuned phase-coherent microwave pump signals, we demonstrated back-action evading (BAE) measurement sensitive to only a single quadrature of the motion. By avoiding the back-action driving in the measured quadrature, such a technique has the potential for precisions surpassing the limit of the zero-point motion. With this method, we achieved a measurement precision of ∼ 100 fm, or 4 times the quantum zero-point motion of the mechanical resonator. We found that the measured quadrature is insensitive to back-action driving by at least a factor of 82 relative to the unmeasured quadrature. We also identified a mechanical parametric amplification effect which arises during the BAE measurement. This effect sets limits on the BAE performance but also mechanically preamplifies the motion, resulting in a position resolution 1.3 times the zero-point motion. We discuss how to overcome the experimental limits set by amplifier noise, pump power and parametric amplification. These results serve to define the path forward for demonstrating truly quantum-limited measurement and non-classical states of motion in a nearly-macroscopic object.