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arXiv:2210.13451 · Physical Review Applied

Superconducting Microsphere Magnetically Levitated in an Anharmonic Potential with Integrated Magnetic Readout

Martí Gutierrez Latorre, Gerard T. Higgins, Achintya Paradkar, Thilo Bauch, Witlef Wieczorek

Published May 12, 2023• 31 citations
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Abstract

The authors present a platform for quantum experiments on levitated particles with masses ranging from nanograms to micrograms. They exploit the Meissner effect to magnetically levitate superconducting microparticles on a chip, in vacuum at ultralow temperatures. Integrated magnetic readout enables coupling to superconducting quantum circuits. This platform allows for precise measurements of force and acceleration, with potential applications in sensing, including the search for dark matter.

DOI
10.1103/physrevapplied.19.054047

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quant-pharXiv:2609.17787•Sep 17, 2026
The authors present a platform for quantum experiments on levitated particles with masses ranging from nanograms to micrograms. They exploit the Meissner effect to magnetically levitate superconducting microparticles on a chip, in vacuum at ultralow temperatures. Integrated magnetic readout enables coupling to superconducting quantum circuits. This platform allows for precise measurements of force and acceleration, with potential applications in sensing, including the search for dark matter.
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.
Levitation of microscopic objects in vacuum combines exceptional environmental isolation with precise control of their dynamics, pushing the limits of sensing and macroscopic quantum physics. In particular, magnetic levitation allows a large range of particle sizes, while avoiding detrimental effects from high-intensity optical trapping beams and electric field noise. However, existing diamagnetic and Meissner levitation approaches are typically constrained by low mechanical eigenfrequencies, limited integrability with other systems due to bulky coils or magnets, and, for Meissner levitation, the need for cryogenic operation. Here, we demonstrate a room-temperature on-chip magnetic levitation platform capable of stably levitating a nanogram (6.5 micrometer radius) ferromagnetic microsphere. The platform is scalable and tunable, and supports librational modes with eigenfrequencies exceeding 10 kHz. Further miniaturization and coupling to solid-state spin qubits could enable cooling to the quantum ground state. Beyond quantum experiments, this architecture enables integrated precision sensing and studies of isolated ferromagnet thermodynamics.
We probe the motion of a 6- μ g magnetically levitated superconducting microsphere using optical interferometry at 3 K , achieving a resolution of the order of 1 nm / Hz , and use the measured signal to feedback-cool its motion. The resolution exceeds the shot-noise limit of 11 pm / Hz primarily due to technical noise arising from the roughness of the particle, in combination with its free rotation. These measurements demonstrate that the combination of interferometric optical readout and superconducting magnetic levitation, together with established techniques of cavity optomechanics, provides all the ingredients required for quantum physics experiments with microgram masses.
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.
Magnetically-levitated superconducting microparticles have been recently proposed as a promising platform for performing quantum experiments with particles in the picogram regime. Here, we demonstrate the superconducting technology to achieve chip-based magnetic levitation of superconducting microparticles. We simulate and fabricate a chip-based magnetic trap capable of levitating superconducting particles with diameters from 0.5 μ\,\muμm to 200 μ\,\muμm. The trap consists of two stacked silicon chips, each patterned with a planar multi-winding superconducting coil made of niobium. The two coils generate a magnetic field resembling a quadrupole near the trap center, in which we demonstrate trapping of a spherical 50μ\muμm diameter SnPb microparticle at temperatures of 4 K and 40 mK.
We introduce a method to suspend an optical micromirror, with a total mass of \SI{30}{\micro\gram}, using superconducting magnetic levitation. The micromirror is formed on a silicon membrane, coated with a high-reflectivity dielectric stack and attached to superconducting microspheres. The object is stably levitated inside a magnetic quadrupole field at cryogenic temperatures. Magnetic feedback on the transverse motion is used to stabilize the position of the levitator within the trapping field, allowing to measure the axial displacement of the levitator using optical interferometry. The system reaches a sensitivity of order \SI{100}{\pico\metre/\sqrt{\hertz}} near the axial trap frequency of \SI{167}{Hz}. This approach enables free-standing mirrors with minimal dissipation and tunable oscillation frequencies, offering a platform for precision sensing and quantum cavity optomechanics in the microgram regime.