{"id":"958a4fab-7151-494b-a1f9-4f7d09759320","arxiv_id":"2605.28479","paper_version":2,"verdict":"UNVERDICTED","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Demonstrates simultaneous feedback cooling of two modes of a levitating milligram permanent magnet in a superconducting trap to sub-2 pm amplitudes and sub-10 mK temperatures using SQUID readout and piezoelectric actuation.","lead":"The paper demonstrates linear feedback cooling of a magnetically levitated milligram permanent magnet to below 2 picometer amplitude and below 10 millikelvin temperature in two translational modes simultaneously. This combines vibration isolation, high-Q resonators, and low-noise SQUID detection in a dilution refrigerator, advancing milligram-scale sensors toward quantum ground-state operation for gravity experiments.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Isolation at 50.6/68 Hz may not be shown to keep residual vibrations below the reported 2 pm cooled amplitudes","rationale":"The reader's weakest assumption directly identifies the experimental precondition required for the headline result. Because the work is an empirical demonstration, confirming that the isolation actually out-performs the achieved amplitude is the single check that would either validate or qualify the central claim; no other internal inconsistency is visible from the supplied material.","tokens_in":1787,"tokens_out":341,"duration_ms":13318,"concrete_test":"Acquire the vibration spectrum at the dilution-refrigerator mixing-chamber flange (sensor removed or mechanically locked) with the same SQUID/lock-in chain; convert to equivalent displacement at the levitated-magnet location using the known trap geometry and compare the integrated power in 1 Hz bands around 50.6 Hz and 68.0 Hz to the 2 pm cooled amplitude; if residual exceeds ~1 pm the isolation claim is insufficient.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The claim of simultaneous feedback cooling to <2 pm amplitude (and <10 mK mode temperature) for the x- and y-modes rests on the 110-130 dB attenuation being sufficient that external seismic/acoustic noise does not set the observed floor. The abstract states the attenuation value and the cryostat mounting but supplies no direct measurement (e.g., base-plate vibration spectrum converted to equivalent displacement at the magnet) showing that residual drive at those frequencies lies below the cooled variance. Without that comparison, the reported amplitudes could be limited by imperfect isolation rather than by the linear feedback itself.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","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.","tokens_in":1906,"tokens_out":491,"duration_ms":23906,"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":[{"comment":"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.","section":"cryostat mounting and isolation performance"}],"minor_comments":[{"comment":"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.","section":"results"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"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.","responses":[{"response":"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_made":"yes","referee_comment":"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."}],"tokens_in":1461,"tokens_out":335,"duration_ms":29215,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper reports linear feedback cooling on a magnetically levitated permanent magnet inside a type-I superconducting trap, read out via SQUID and cooled with piezoelectric actuation. They achieve simultaneous cooling of the x- and y-modes at 50.6 Hz and 68 Hz to below 2 pm amplitude and below 10 mK mode temperature, with Q factors of 3.8e6 and 5.5e6. The whole setup sits in a dilution refrigerator with 110-130 dB vibrational attenuation at those frequencies.\n\nWhat is actually new is the dual-mode result at milligram scale with those specific numbers. Prior work has shown levitated magnets as gravity sensors and separate cooling techniques, but this combines the trap, SQUID readout, feedback, and fridge isolation into one run that hits both amplitude and temperature targets at once. The measured resonance frequencies and Q values are straightforward to verify from the data.\n\nThe soft spot is the isolation performance. The abstract states the attenuation level and the mounting, but does not include a direct comparison of the base-plate vibration spectrum converted to equivalent displacement at the magnet position. Without that, it is possible the reported 2 pm floor is still set by external drive rather than the feedback loop itself. If the full manuscript has those traces or an equivalent calculation, the concern disappears; otherwise it is a real gap that needs addressing.\n\nThe work is for groups doing levitated optomechanics or macroscopic quantum sensors aimed at gravity tests. A reader who needs practical numbers on milligram-scale cooling and SQUID readout will find usable details here.\n\nIt deserves peer review. The central claim is an experimental measurement rather than a derivation, and the setup is reproducible in principle. A referee can check the isolation data and ask for any missing error bars or raw spectra.","headline":"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.","tokens_in":2451,"tokens_out":462,"would_cite":false,"duration_ms":18495,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Linear feedback cooling brings a levitated milligram gravity sensor below 2 picometer amplitude in two modes at once.","keywords":["levitated magnet","feedback cooling","gravity sensor","SQUID readout","superconducting trap","dilution refrigerator","picometer amplitude","quantum ground state"],"falsifier":"A direct measurement of the position spectral density with feedback engaged that shows rms amplitudes remaining above 2 picometers at either resonance frequency.","tokens_in":2674,"feed_emoji":"🧲","tokens_out":756,"duration_ms":18614,"temperature":0.7,"pith_summary":"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.","feed_headline":"Feedback cooling reaches below 2 picometers on levitated milligram sensor","feed_subtitle":"Two translational modes of a magnetically levitated permanent magnet are cooled to sub-10 millikelvin inside a vibration-isolated dilution r","key_machinery":"Linear feedback loop that uses the SQUID readout of the levitated magnet's motion to drive a piezoelectric actuator at the two resonance frequencies.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Feedback cools levitated magnet modes below 2 picometer amplitude","Linear feedback achieves 2 pm cooling on levitating magnet","Two modes cooled simultaneously to below 2 pm in levitated sensor","Levitated milligram sensor feedback cooled below 2 picometers","Milligram gravity sensor reaches picometer amplitude via feedback"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Feedback cools levitated magnet modes below 2 picometer amplitude","Linear feedback achieves 2 pm cooling on levitating magnet","Two modes cooled simultaneously to below 2 pm in levitated sensor","Levitated milligram sensor feedback cooled below 2 picometers","Milligram gravity sensor reaches picometer amplitude via feedback"]},"model":"grok-4.3","cost_usd":0.004677,"raw_usage":{"total_tokens":2260,"prompt_tokens":725,"num_sources_used":0,"completion_tokens":82,"cost_in_usd_ticks":46765500,"prompt_tokens_details":{"text_tokens":725,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1453,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":725,"tokens_out":82,"duration_ms":10079,"temperature":1.0,"reasoning_tokens":1453,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-02T23:14:13.408352+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct measurement of the position spectral density with feedback engaged that shows rms amplitudes remaining above 2 picometers at either resonance frequency.","supporting_citations":[],"review_version":2}