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arXiv:2605.09632

A Superconducting Levitating Oscillator with < 1 $μ$Hz Resonance Linewidth

M. Arrayás, J. L. Trueba, C. Uriarte, J. Clothier, C. C. E. Elmy, R. Schanen, D. E. Zmeev, Š. Midlik

quant-phphysics.ins-detSubmitted May 10, 2026• Announced May 12, 2026
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Abstract

Experiments aimed at quantifying the interface between quantum and classical physics necessarily require a high degree of isolation from the environment: wavefunction collapse and quantum gravity effects at laboratory scales are predicted to be very subtle. Ideally, such tests would be performed in a closed system at extremely low temperatures in order to rule out any external influence and thermal fluctuations. Cryogenic levitated macroscopic bodies are excellent candidates for an accurate laboratory approximation of such systems, as a tether to another body would violate the requirement for the system to be fully closed. Here we report a significant milestone on the way to a practically suitable approximation of such closed system. We have built a milligram-mass superconducting oscillator operating at millikelvin temperatures showing extremely low dissipation rate, with the oscillator ring-down time exceeding 110 hours. This corresponds to the resonance linewidth of less than 0.8 $μ$Hz. The experimental setup is highly tunable and is compatible with adiabatic nuclear demagnetisation, promising even lower temperatures and lower dissipation levels in the future. We demonstrate the capability of our device by measuring drag from $^3$He impurities in superfluid $^4$He at a level of $\sim10^{-8}$ with the drag force in the femtonewton range.

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•Apr 13, 2026•0 citations
A Superconducting Levitating Oscillator with < 1 μμμHz Resonance Linewidth
Experiments aimed at quantifying the interface between quantum and classical physics necessarily require a high degree of isolation from the environment: wavefunction collapse and quantum gravity effects at laboratory scales are predicted to be very subtle. Ideally, such tests would be performed in a closed system at extremely low temperatures in order to rule out any external influence and thermal fluctuations. Cryogenic levitated macroscopic bodies are excellent candidates for an accurate laboratory approximation of such systems, as a tether to another body would violate the requirement for the system to be fully closed. Here we report a significant milestone on the way to a practically suitable approximation of such closed system. We have built a milligram-mass superconducting oscillator operating at millikelvin temperatures showing extremely low dissipation rate, with the oscillator ring-down time exceeding 110 hours. This corresponds to the resonance linewidth of less than 0.8 μμμHz. The experimental setup is highly tunable and is compatible with adiabatic nuclear demagnetisation, promising even lower temperatures and lower dissipation levels in the future. We demonstrate the capability of our device by measuring drag from 3^33He impurities in superfluid 4^44He at a level of ∼10−8\sim10^{-8}∼10−8 with the drag force in the femtonewton range.
We report the levitation of a superconducting lead-tin sphere with 100 μm diameter (corresponding to a mass of 5.6 μg) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240 Hz. The center-of-mass motion of the sphere is monitored magnetically using a dc superconducting quantum interference device as well as optically and exhibits quality factors of up to 2.6×10^{7}. We also demonstrate 3D magnetic feedback control of the motion of the sphere. The setup is housed in a dilution refrigerator operating at 15 mK. By implementing a cryogenic vibration isolation system, we can attenuate environmental vibrations at 200 Hz by approximately 7 orders of magnitude. The combination of low temperature, large mass, and high quality factor provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times.
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⋅1063.8 \cdot 10^63.8⋅106 and 5.5⋅1065.5 \cdot 10^65.5⋅106 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.
Near-field force measurements at submicron separations can probe Casimir effects and hypothetical short-range interactions, but require cryogenic operation and stable, \textit{in situ} control of separation-dependent backgrounds. We propose a self-calibrating quantum force-gradient sensor in which a ferromagnetic microsphere is Meissner-levitated above a type-I superconducting plane, while a bias magnetic field reproducibly tunes the equilibrium gap for in situ separation scans without mechanical approach. The force gradient is encoded as a resonance-frequency shift tracked by a phase-locked loop, and the motion is read out with a SQUID-coupled, flux-tunable microwave resonator that provides adjustable measurement strength without optical heating. Using the input--output formalism, we derive the conditions for reaching the standard quantum limit (SQL) and identify a counterintuitive scaling law: because displacement-to-flux transduction increases with microsphere size, larger microspheres require fewer photons to reach the SQL, enabling a pathway to macroscopic quantum metrology. We quantify the trade-off between suppression of electrostatic patch potentials (via Au coating) and eddy-current dissipation, project force sensitivities of ∼10−19 N Hz−1/2\sim 10^{-19}\,\rm{N\,Hz^{-1/2}}∼10−19NHz−1/2 at millikelvin temperatures, and outline protocols to extract Casimir pressure and constrain Yukawa-type deviations from Newtonian gravity over 0.10.10.1--10 μm10\,μ\mathrm{m}10μm.
We present a cavity-electromechanical system comprising a superconducting quantum interference device which is embedded in a microwave resonator and coupled via a pickup loop to a 6 - μ g magnetically levitated superconducting sphere. The motion of the sphere in the magnetic trap induces a frequency shift in the SQUID-cavity system. We use microwave spectroscopy to characterize the system, and we demonstrate that the electromechanical interaction is tunable. The measured displacement sensitivity of 10 − 7 m / Hz defines a path towards ground-state cooling of levitated particles with Planck-scale masses at millikelvin environment temperatures. Published by the American Physical Society 2024
Magnetically levitated superconducting microparticles provide a promising platform for fundamental quantum experiments and quantum-limited sensing. In the Meissner state, the levitated particle is trapped without mechanical clamping, allowing its center-of-mass motion to exhibit ultralow dissipation. The particle's displacement can be read out dispersively via magnetic flux coupling to superconducting resonators. A challenge for magnetomechanical coupling is to realize a flux-tunable microwave circuit that provides strong flux-to-frequency transduction, low dissipation, and a sufficiently large linear operating range for readout and cooling. This thesis develops and characterizes a chip-based superconducting platform for realizing this transduction.Chip-based levitation of a superconducting microparticle is demonstrated at 40 mK. Passive cryogenic vibration isolation is developed to increase the mechanical quality factors of the levitated particle. For coupling to a microwave circuit, a superconducting flip-chip process based on indium microspheres was developed. The need for Au passivation of Nb or NbN under-bump metallization is demonstrated, and indium-based superconducting interconnects are shown to carry ampere-scale currents. Flux-tunable resonators with 100-200 µm SQUID loops and integrated input coils are designed, fabricated, and characterized. A peak flux responsivity of 20 GHz/Φ₀ is achieved, with one flux quantum modulation requiring only 10-20 µA of input-coil current. Two integrated flux-biasing architectures are developed with flip-chip and on-chip input coils, achieving a total flux transfer efficiency of 1.6%. Junction asymmetry is shown to suppress branch-switching behavior associated with finite SQUID screening.Together, these results establish the superconducting subsystems required for dispersive microwave readout of the center-of-mass motion of a levitated microparticle. Such a magnetomechanical coupling provides a route toward cooling the center-of-mass motion to the ground state, paving the way for the preparation of nonclassical motional states. More broadly, such systems are well-suited for quantum-limited force and acceleration sensing, as well as for probing quantum physics in a previously unexplored mass regime.