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arxiv: 2605.28479 · v1 · pith:4VBLFXVDnew · 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

Pith reviewed 2026-06-29 11:33 UTC · model grok-4.3

classification 🪐 quant-ph
keywords levitated magnetfeedback coolingSQUID readoutsuperconducting trapgravity sensordilution refrigeratorpicometer amplitudemode temperature
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The pith

Linear feedback cooling achieves below 2 picometer amplitudes and below 10 millikelvin temperatures for two modes of a magnetically levitated milligram sensor.

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

The paper demonstrates that linear feedback can cool two translational modes of a magnetically levitated permanent magnet to amplitudes below 2 picometers and mode temperatures below 10 millikelvin at the same time. This uses a type I superconducting trap for levitation, a SQUID for position readout, and a piezoelectric actuator for feedback, all inside a dilution refrigerator providing 110-130 dB of vibration isolation. The modes oscillate at 50.6 and 68.0 Hz with quality factors of millions. Reaching these levels combines state-of-the-art isolation, high-Q mechanics, and low-noise detection as a step toward ground-state cooling for future gravity experiments on quantum superpositions.

Core claim

Linear feedback cooling of a magnetically levitated gravity sensor reaches below 2 picometer amplitude and below 10 millikelvin mode temperature for two translational modes simultaneously. The sensor is a levitating permanent magnet in a type I superconducting trap, where its resonance frequencies are measured with a superconducting coil coupled to a DC SQUID. The signal is processed with a lock-in amplifier and a feedback signal drives a piezoelectric actuator to cool the modes at 50.6 and 68.0 Hz, which have Q factors of 3.8 million and 5.5 million. The entire setup sits inside a dry dilution refrigerator with 110-130 dB vibrational attenuation at these frequencies.

What carries the argument

Linear feedback cooling driven by the position signal from a DC SQUID readout to a piezoelectric actuator on a levitated permanent magnet inside a type I superconducting trap.

If this is right

  • Simultaneous cooling of two translational modes is possible with the SQUID readout and piezoelectric feedback.
  • The high Q factors and vibration isolation support reaching the reported amplitude and temperature limits.
  • Future improvements to the setup can enable quantum ground state cooling of the levitated particle.
  • The cooled levitated particle remains usable as a gravitational sensor.

Where Pith is reading between the lines

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

  • Ground-state cooling of this system would permit direct tests of gravity acting on macroscopic quantum superpositions.
  • The same feedback approach may extend to cooling rotational or other degrees of freedom in the levitated magnet.
  • Reduced thermal motion at these levels could increase the force sensitivity of the gravity sensor beyond current thermal-noise limits.

Load-bearing premise

The 110-130 dB vibrational attenuation inside the dilution refrigerator combined with the SQUID readout noise floor is sufficient to allow the reported feedback cooling to reach the stated amplitude and temperature limits without other heating mechanisms dominating.

What would settle it

An independent measurement finding either mode amplitude above 2 picometers or mode temperature above 10 millikelvin when the described feedback is active would falsify the cooling performance.

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 ↗
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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reports an experimental demonstration of simultaneous linear feedback cooling of two translational modes (50.6 Hz and 68.0 Hz) of a magnetically levitated milligram permanent magnet in a type-I superconducting trap. Using DC SQUID readout of a superconducting coil and piezoelectric actuation, the authors achieve amplitudes below 2 picometers and mode temperatures below 10 mK for both the x- and y-modes inside a dry dilution refrigerator with 110-130 dB vibrational isolation at the relevant frequencies. The modes exhibit Q factors of 3.8×10^6 and 5.5×10^6. The work discusses prospects for future quantum ground-state cooling toward gravitational sensing applications.

Significance. If the reported performance metrics are substantiated with full calibration and data, the result constitutes a meaningful technical advance in levitated mechanical sensors. It shows the practical integration of milligram-scale high-Q resonators, extreme vibrational isolation, and low-noise SQUID detection to reach picometer amplitudes and millikelvin temperatures on multiple modes simultaneously, directly relevant to proposals for quantum gravity experiments.

major comments (2)
  1. [Abstract] Abstract: The headline claims of amplitudes below 2 pm and mode temperatures below 10 mK are stated without error bars, raw spectral data, position calibration details, or the explicit procedure used to convert the SQUID signal into these quantities.
  2. [Experimental setup] Experimental setup paragraph: The claim that 110-130 dB vibrational attenuation plus the SQUID noise floor is sufficient to reach the stated limits without other heating mechanisms dominating is presented without quantitative estimates of residual acceleration noise, heating rates, or direct measurements confirming that these sources do not set the observed floor.
minor comments (1)
  1. [Abstract] The abstract states that six resonance frequencies are measured but provides Q factors and cooling results for only two; a short statement on the status of the remaining modes would improve completeness without altering the central claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its significance. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The headline claims of amplitudes below 2 pm and mode temperatures below 10 mK are stated without error bars, raw spectral data, position calibration details, or the explicit procedure used to convert the SQUID signal into these quantities.

    Authors: The abstract is intended as a concise summary of the principal results. The position calibration of the SQUID readout, the explicit conversion procedure from voltage to displacement and temperature, the raw spectral data, and the associated uncertainties (including error bars on the reported amplitudes and temperatures) are all provided in the main text, specifically in the sections describing the readout chain, data acquisition, and results, together with the corresponding figures. To address the referee's concern about clarity, we will revise the abstract to include a brief parenthetical reference to the calibration procedure detailed in the manuscript body. revision: yes

  2. Referee: [Experimental setup] Experimental setup paragraph: The claim that 110-130 dB vibrational attenuation plus the SQUID noise floor is sufficient to reach the stated limits without other heating mechanisms dominating is presented without quantitative estimates of residual acceleration noise, heating rates, or direct measurements confirming that these sources do not set the observed floor.

    Authors: We agree that the manuscript would benefit from explicit quantitative support for this claim. In the revised version we will add estimates of residual acceleration noise derived from the measured vibrational isolation spectrum, compare these to the observed displacement floor, and include order-of-magnitude heating-rate calculations for the dominant environmental sources to demonstrate that they remain below the level set by the SQUID noise floor at the reported amplitudes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental report only

full rationale

This paper reports an experimental demonstration of linear feedback cooling on a magnetically levitated milligram-scale permanent magnet inside a dilution refrigerator. The central results (amplitudes <2 pm, mode temperatures <10 mK, Q factors of 3.8e6 and 5.5e6 at 50.6 Hz and 68.0 Hz) are obtained from direct SQUID readout of resonance frequencies, lock-in detection, and piezoelectric feedback, with vibrational isolation quantified at 110-130 dB. No derivation chain, fitted parameter renamed as prediction, self-definitional relation, or load-bearing self-citation is present. The position calibration and temperature inference follow standard relations from measured displacement spectra and are not reduced to quantities defined by the authors' own ansatz or prior self-citations. The result is self-contained against external benchmarks (measured isolation, SQUID noise floor).

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work is an experimental demonstration that relies on established techniques in magnetic levitation, SQUID readout, and cryogenic vibration isolation; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Standard performance of DC SQUID position detection and piezoelectric actuation in a type I superconducting trap holds under the reported cryogenic conditions.
    The cooling result depends on these background capabilities being adequate.

pith-pipeline@v0.9.1-grok · 5789 in / 1253 out tokens · 34504 ms · 2026-06-29T11:33:48.845793+00:00 · methodology

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Reference graph

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