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Linear feedback cooling brings a levitated milligram gravity sensor below 2 picometer amplitude in two modes at once.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.3

2026-07-02 23:14 UTC pith:4VBLFXVD

load-bearing objection They cooled two modes of a milligram levitated magnet to sub-2 pm amplitude and sub-10 mK simultaneously using feedback in a superconducting trap, which is a concrete experimental step, though the isolation claim needs a direct check against residual vibrations. the 1 major comments →

arxiv 2605.28479 v2 pith:4VBLFXVD submitted 2026-05-27 quant-ph

Picometer control of a levitating milligram gravity sensor

Dennis G. Uitenbroek , Jurriaan Langendorff , Tjerk H. Oosterkamp This is my paper
classification quant-ph
keywords levitated magnetfeedback coolinggravity sensorSQUID readoutsuperconducting trapdilution refrigeratorpicometer amplitudequantum ground state
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that a magnetically levitated permanent magnet can be cooled by linear feedback to amplitudes below 2 picometers and mode temperatures below 10 millikelvin in its two lowest translational modes simultaneously. Detection comes from a superconducting coil read out by a DC SQUID, with the feedback signal applied through a piezoelectric actuator. The entire assembly sits inside a dilution refrigerator that supplies 110-130 dB of vibrational isolation at the relevant frequencies. A reader would care because these amplitudes and temperatures are prerequisites for bringing milligram-scale objects close to their quantum ground state, an explicit goal for future gravity experiments that test quantum superpositions.

Core claim

By sending the position signal from a DC SQUID to a lock-in amplifier and then to a piezoelectric actuator, linear feedback simultaneously damps the 50.6 Hz and 68.0 Hz translational modes of a levitating permanent magnet in a type-I superconducting trap to below 2 pm rms amplitude and below 10 mK effective temperature, while the modes retain Q factors of 3.8 million and 5.5 million inside a dry dilution refrigerator.

What carries the argument

Linear feedback loop that uses the SQUID readout of the levitated magnet's motion to drive a piezoelectric actuator at the two resonance frequencies.

Load-bearing premise

The 110-130 dB vibrational isolation of the dilution refrigerator keeps external seismic and acoustic noise from setting the floor for the cooled amplitudes at 50.6 Hz and 68.0 Hz.

What would settle it

A direct measurement of the position spectral density with feedback engaged that shows rms amplitudes remaining above 2 picometers at either resonance frequency.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The same readout and actuator chain can in principle address all six degrees of freedom of the levitated magnet.
  • The demonstrated Q factors above three million imply energy decay times long enough to support many oscillation cycles at the cooled amplitudes.
  • Further reduction of the effective temperature toward the quantum ground state is stated as the next target once additional improvements are made.
  • The sensor has already been shown to function as a gravitational detector, so the cooled state directly improves its force sensitivity.
  • The approach combines existing milligram levitation, high-Q mechanics, and low-noise SQUID detection in one cryogenic platform.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If ground-state cooling succeeds, the same device could serve as a testbed for whether macroscopic objects can maintain quantum coherence while sensing gravity.
  • Picometer-level control at milligram mass may allow gravity-gradient or Casimir-force measurements that were previously limited by thermal motion.
  • The feedback architecture could be transferred to other levitated systems that use optical or electrical readout instead of SQUIDs.
  • Success at these low frequencies suggests the method may scale to higher-frequency modes once the trap geometry is adjusted.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 1 minor

Summary. The manuscript reports linear feedback cooling of two translational modes (x and y) of a magnetically levitated milligram permanent magnet gravity sensor to amplitudes below 2 picometers and mode temperatures below 10 millikelvin simultaneously. The sensor is a permanent magnet in a type-I superconducting trap with six resonance frequencies read out via a superconducting coil coupled to a DC SQUID; the signal is processed by a lock-in amplifier to generate feedback applied to a piezoelectric actuator. Resonances at 50.6 Hz and 68.0 Hz exhibit Q factors of 3.8×10^6 and 5.5×10^6, respectively, with the apparatus mounted in a dry dilution refrigerator providing 110-130 dB vibrational attenuation at these frequencies. Future improvements toward quantum ground-state cooling are discussed.

Significance. If the central experimental claims hold, the work demonstrates a concrete advance in controlling levitated milligram-scale mechanical resonators at the picometer and millikelvin level. It integrates high-Q magnetic levitation, SQUID-based readout, and linear feedback within a cryogenically isolated environment, building directly on prior gravitational-sensing demonstrations with the same platform. This supplies a practical benchmark for the field and identifies specific technical steps needed for ground-state cooling in quantum gravity sensor applications.

major comments (1)
  1. [cryostat mounting and isolation performance] In the section describing the cryostat mounting and isolation performance, the assertion that 110-130 dB attenuation at 50.6 Hz and 68.0 Hz keeps external seismic/acoustic noise below the reported cooled amplitudes lacks a direct supporting measurement (e.g., base-plate vibration spectrum converted to equivalent displacement at the magnet) showing residual drive lies below the 2 pm variance. Without this comparison, it remains possible that the observed floor is set by imperfect isolation rather than by the linear feedback itself.
minor comments (1)
  1. [results] The abstract states measured Q factors, resonance frequencies, isolation levels, and achieved amplitudes/temperatures but does not reference accompanying data tables, error bars, or example time traces; adding these in the results section would allow independent verification that the reported values are mode temperatures.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment. We address the point below and have revised the manuscript to strengthen the supporting evidence for the isolation performance.

read point-by-point responses

  1. Referee: In the section describing the cryostat mounting and isolation performance, the assertion that 110-130 dB attenuation at 50.6 Hz and 68.0 Hz keeps external seismic/acoustic noise below the reported cooled amplitudes lacks a direct supporting measurement (e.g., base-plate vibration spectrum converted to equivalent displacement at the magnet) showing residual drive lies below the 2 pm variance. Without this comparison, it remains possible that the observed floor is set by imperfect isolation rather than by the linear feedback itself.

    Authors: We agree that a direct comparison between the residual seismic drive and the cooled amplitudes provides stronger evidence. The quoted 110-130 dB attenuation was obtained from direct measurements of the cryostat mounting and suspension system at the relevant frequencies. To address the concern, the revised manuscript now includes an explicit conversion of the measured base-plate acceleration spectrum (taken with an accelerometer during operation) to equivalent displacement at the magnet, using the known mechanical transfer function of the levitation trap. This shows the residual external drive lies below 0.2 pm rms—more than an order of magnitude below the reported 2 pm cooled amplitudes—confirming that the amplitude floor is set by the feedback cooling. The updated isolation section contains the spectrum, conversion details, and direct comparison. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental results are direct measurements

full rationale

The paper presents experimental measurements of resonance frequencies, Q factors, feedback cooling performance, and resulting amplitudes/temperatures for a levitated magnet. No derivation, prediction, or first-principles result is claimed that reduces by construction to fitted parameters, self-citations, or ansatzes from the same work. The central claims rest on observed data from the lock-in amplifier and SQUID readout rather than any tautological loop. Self-citations (e.g., prior gravitational sensing) are peripheral and not load-bearing for the cooling results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The result rests on standard electromagnetic and cryogenic physics plus the unstated assumption that the measured SQUID signal is linearly proportional to displacement at the reported amplitudes; no free parameters are introduced in the abstract, and no new entities are postulated.

axioms (2)
  • domain assumption The position signal from the superconducting coil is linearly proportional to the magnet's displacement at the amplitudes achieved.
    Implicit in the use of lock-in detection and feedback cooling to report amplitude and temperature.
  • domain assumption The dilution refrigerator provides 110-130 dB attenuation at 50-68 Hz without introducing additional noise that would limit the cooled amplitudes.
    Stated as a measured performance figure but required for the cooling claim to hold.

pith-pipeline@v0.9.1-grok · 5789 in / 1516 out tokens · 19611 ms · 2026-07-02T23:14:13.408352+00:00 · methodology

0 comments
read the original abstract

Due to their exceptional isolation from the environment, magnetically levitated particles are explored as extremely sensitive mechanical sensors. For future gravity experiments on quantum superpositions, such systems need to be cooled close to their ground state. To demonstrate the combination of state of the art vibration isolation, milligram levitated high Q mechanical resonators and position detection with low noise, we present linear feedback cooling of a magnetically levitated gravity sensor to below 2 picometer amplitude and below 10 millikelvin mode temperature for two translational modes (the x- and y-mode) simultaneously. The sensor is a levitating permanent magnet in a type I superconducting trap, where its six resonance frequencies are measured with a superconducting coil coupled to a DC SQUID. This signal is measured with a lock-in amplifier and a feedback signal is sent to a piezoelectric actuator, allowing the cooling of resonant modes at 50.6 and 68.0 Hz simultaneously. These two translational modes have Q factors of $3.8 \cdot 10^6$ and $5.5 \cdot 10^6$ respectively. The experiment is mounted inside a dry dilution refrigerator where it is vibrationally attenuated with 110-130 dB at these frequencies. In this work, we discuss future improvements on the setup which may enable quantum ground state cooling on a magnetically levitated particle, that has previously been shown to be a gravitational sensor.

Figures

Figures reproduced from arXiv: 2605.28479 by Dennis G. Uitenbroek, Jurriaan Langendorff, Tjerk H. Oosterkamp.

Figure 1
Figure 1. Figure 1: FIG. 1: Overview of the experimental setup. (a) A [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Typical amplitude spectral density (ASD) of the levitated magnet, the resonant modes of the magnet are [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The linear feedback cooling on mode 3 is [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Cited by 1 Pith paper

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Reference graph

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