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One-milligram torsional pendulum toward experiments at the quantum-gravity interface

Sofia Agafonova, Pere Rossello, Manuel Mekonnen, Onur Hosten

Abstract

Probing the possibility of entanglement generation through gravity offers a path to tackle the question of whether gravitational fields possess a quantum mechanical nature. A potential realization necessitates systems with low-frequency dynamics at an optimal mass scale, for which the microgram-to-milligram range is a strong contender. Here, after refining a figure-of-merit for the problem, we present a 1-milligram torsional pendulum operating at 18 Hz. We demonstrate laser cooling its motion from room temperature to 240~microkelvins, surpassing by over 20-fold the coldest motions attained for oscillators ranging from micrograms to kilograms. We quantify and contrast the utility of the current approach with other platforms. The achieved performance and large improvement potential highlight milligram-scale torsional pendulums as a powerful platform for precision measurements relevant to future studies at the quantum-gravity interface.

One-milligram torsional pendulum toward experiments at the quantum-gravity interface

Abstract

Probing the possibility of entanglement generation through gravity offers a path to tackle the question of whether gravitational fields possess a quantum mechanical nature. A potential realization necessitates systems with low-frequency dynamics at an optimal mass scale, for which the microgram-to-milligram range is a strong contender. Here, after refining a figure-of-merit for the problem, we present a 1-milligram torsional pendulum operating at 18 Hz. We demonstrate laser cooling its motion from room temperature to 240~microkelvins, surpassing by over 20-fold the coldest motions attained for oscillators ranging from micrograms to kilograms. We quantify and contrast the utility of the current approach with other platforms. The achieved performance and large improvement potential highlight milligram-scale torsional pendulums as a powerful platform for precision measurements relevant to future studies at the quantum-gravity interface.
Paper Structure (4 sections, 5 equations, 3 figures)

This paper contains 4 sections, 5 equations, 3 figures.

Figures (3)

  • Figure 1: Experimental setup.a The in-vacuum pendulum. Insets: Tapered suspension fiber ends and the pendulum mirror bar. b The optical setup. PBS: polarizing beam splitter, $\lambda/2$: half-wave plate, $\lambda/4$: quarter-wave plate, AOM: acousto-optic modulator, SG: signal generator, VA: variable attenuator, SA: spectrum analyzer, FB: feedback circuit, PD: photodetector, QPD: quadrant PD, L2H(V): horizontal (vertical) cylindrical lens with 200 mm (60 mm) focal length, L1(3, 4): spherical lens with 4.5 mm (10 mm, 4.0 mm) focal length. c Steady-state yaw noise spectrum (blue) compared to thermal noise models (dashed lines) with structural or viscous damping. Inset: close-up of the resonance peak, orange data: detection noise spectrum compared to theoretical laser shot-noise PhysRevX.13.011018, "zp" curve: theoretical spectrum for quantum zero-point fluctuations associated with the yaw motion for reference. The parasitic 2.27-Hz peak is due to the residual swing motion sensitivity in the yaw channel. The "detection noise" model incorporates a variable "white + 1/f" noise to fit the data above 8 Hz. d Ring-down measurement of the 6.72-Hz yaw oscillations. e Probe beam profile across the lens system for horizontal (red) and vertical (blue) directions. Top; solid lines: spot size evolution, dashed lines: centroid evolution for a 100-$\mu\text{rad}$ illustrative yaw (red) or pitch (blue) rotation of the pendulum. Bottom; tilt sensitivity parameter $\mathcal{S}$.
  • Figure 2: Feedback control of the motion.a Experimental effective susceptibilities as the resonance frequency of the pendulum is shifted under feedback control. Normalization is to the DC value of the feedback-free susceptibility. b Noise spectral densities for different feedback damping strengths for the pendulum shifted to 18 Hz. Data points: mean spectral density within each 2.4-Hz frequency bin, error bars: $\pm1$ standard deviation within each bin, solid lines: theoretical noise models with excess vibration noise as a fit parameter, error bands: variation in the model curves due to the full-range of lab vibration noise level changes, detection noise: same as Fig. \ref{['fig:setup']}. Inset: coherence angles $\xi_\theta$ and pendulum-tip coherence lengths $\xi$. Side panels show the noise breakdown for representative damping strengths. Solid lines: total noise, dash-dotted lines: theoretical thermal noise given the effective susceptibilities, dashed lines: theoretical imprinted measurement noise, dotted lines: extracted white-torque-noise equivalent vibration noise.
  • Figure 3: Comparison to state-of-the-art mechanical quantum control experiments for utility at the quantum-gravity interface. Colors encode oscillator masses. Experiments in a cryogenic environment are tagged with snow flakes. Experiments: a nanosphere rossi2024, b nanosphere doi:10.1126/science.aba3993, c nanobeam Wilson2015, d microsphere monteiro2020, e membrane Rossi2018, f cantilever PhysRevLett.130.033601, g membrane PhysRevA.92.061801, h superconducting microsphere PhysRevLett.131.043603, i acoustic resonator bild2023, j pendulum PhysRevA.94.033822, k pendulum PhysRevLett.99.160801, l LIGO pendulums doi:10.1126/science.abh2634, m bar resonator PhysRevLett.101.033601. For 'This work', projected future performances at different levels are also indicated; see main text.