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Meissner levitation of a permanent magnet within a superconducting radio frequency cavity

Nabin K. Raut, Jeffery Miller, R. Y. Chiao, Jay E. Sharping

Published Jan 5, 2021• 0 citations
OpenAlex

Abstract

We report the first experimental demonstration of Meissner-effect levitation of a millimeter-scale neodymium magnet within a cm-scale superconducting aluminum coaxial quarter-wave stub cavity. The coaxial mode's resonance frequency shifts as a function of the levitation height of the magnet, giving an estimate of the magnet's position and mechanical motion. The levitation height sensitivity is as large as 400 MHz/mm, where the total frequency shift is 1% of the bare cavity resonance. We observe levitation of magnets with remanences up to 140 times stronger than the critical field of the aluminum, and our experiments and simulations reveal that both the levitation height and levitation temperature increase with the strength of the magnet. This novel magnet-cavity system provides a means to couple the low-frequency mechanical motion of the magnet with other objects, such as magnons and transmons, which are used for quantum information processing.

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We report on the behavior of a superconducting microwave cavity containing levitated permanent magnets having a range of magnet strengths. By observing the changes in the cavity’s loaded quality factor and resonance frequency as functions of temperature and magnet remanence, we gain an understanding of the transient motion of the magnet as well as its steady-state levitation height when the temperature drops below 1 K. Experimental measurements of Meissner-effect levitation within a 10 GHz superconducting aluminum coaxial quarter-wave stub cavity are performed for a sequence of identically shaped millimeter-scale neodymium magnets having varying strengths. Magnet levitation within the cavity is accompanied by both gradual and abrupt shifts in the resonance frequency (with a height sensitivity as large as 400 MHz/mm) as well as changes in the total quality factor (8%-17%) as a function of temperature during the superconducting transition of the aluminum cavity. Prior to magnet motion and levitation, the Q of the cavity changes quadratically with temperature, as expected, as the walls of the cavity undergo the superconducting transition. We observe, however, a deviation from the quadratic trend which is attributable to magnet movement within the cavity. Such an electromechanical system is a transducer between mechanical and microwave oscillators enabling coupling of low-frequency mechanical motion of the magnet to other quantum objects, such as magnons and transmons, which are used for sensing and quantum information processing.

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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.

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Magnetic levitation offer passive levitation of massive objects for use in advanced inertia sensors, for the generation of non-classical macroscopic motional states, and towards the table-top testing of low energy gravity with quantum mechanics. Magnons, a quanta of spin wave, couple to many physical quantities and strongly to electromagnetic fields, even at room temperature. In this work we demonstrate the stable trapping of a small YIG sphere using a magnetic Paul trap. We present a classical stability analysis of a magnetic Paul trap and show the stability diagram for all mechanical degrees of freedom. We show that coupling between librational and translational modes changes the stability region. We experimentally levitate the soft magnet yttrium iron garnet at room temperature obtaining Q-factors of $\sim25$ and secular frequencies $15.8$ Hz and $17.2$ Hz. We provide numerical estimates of the achievable enhanced coupling between the center-of-mass motion and excited magnon modes, with a cooperativity above unity despite strong mechanical damping, indicating potential applications in quantum information processing, quantum interconnects and quantum memories.

quant-pharXiv:2608.12752•Aug 14, 2026
We report the first experimental demonstration of Meissner-effect levitation of a millimeter-scale neodymium magnet within a cm-scale superconducting aluminum coaxial quarter-wave stub cavity. The coaxial mode's resonance frequency shifts as a function of the levitation height of the magnet, giving an estimate of the magnet's position and mechanical motion. The levitation height sensitivity is as large as 400 MHz/mm, where the total frequency shift is 1% of the bare cavity resonance. We observe levitation of magnets with remanences up to 140 times stronger than the critical field of the aluminum, and our experiments and simulations reveal that both the levitation height and levitation temperature increase with the strength of the magnet. This novel magnet-cavity system provides a means to couple the low-frequency mechanical motion of the magnet with other objects, such as magnons and transmons, which are used for quantum information processing.
We report on the behavior of a superconducting microwave cavity containing levitated permanent magnets having a range of magnet strengths. By observing the changes in the cavity’s loaded quality factor and resonance frequency as functions of temperature and magnet remanence, we gain an understanding of the transient motion of the magnet as well as its steady-state levitation height when the temperature drops below 1 K. Experimental measurements of Meissner-effect levitation within a 10 GHz superconducting aluminum coaxial quarter-wave stub cavity are performed for a sequence of identically shaped millimeter-scale neodymium magnets having varying strengths. Magnet levitation within the cavity is accompanied by both gradual and abrupt shifts in the resonance frequency (with a height sensitivity as large as 400 MHz/mm) as well as changes in the total quality factor (8%-17%) as a function of temperature during the superconducting transition of the aluminum cavity. Prior to magnet motion and levitation, the Q of the cavity changes quadratically with temperature, as expected, as the walls of the cavity undergo the superconducting transition. We observe, however, a deviation from the quadratic trend which is attributable to magnet movement within the cavity. Such an electromechanical system is a transducer between mechanical and microwave oscillators enabling coupling of low-frequency mechanical motion of the magnet to other quantum objects, such as magnons and transmons, which are used for sensing and quantum information processing.
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
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.
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.
Magnetic levitation offer passive levitation of massive objects for use in advanced inertia sensors, for the generation of non-classical macroscopic motional states, and towards the table-top testing of low energy gravity with quantum mechanics. Magnons, a quanta of spin wave, couple to many physical quantities and strongly to electromagnetic fields, even at room temperature. In this work we demonstrate the stable trapping of a small YIG sphere using a magnetic Paul trap. We present a classical stability analysis of a magnetic Paul trap and show the stability diagram for all mechanical degrees of freedom. We show that coupling between librational and translational modes changes the stability region. We experimentally levitate the soft magnet yttrium iron garnet at room temperature obtaining Q-factors of ∼25\sim25∼25 and secular frequencies 15.815.815.8 Hz and 17.217.217.2 Hz. We provide numerical estimates of the achievable enhanced coupling between the center-of-mass motion and excited magnon modes, with a cooperativity above unity despite strong mechanical damping, indicating potential applications in quantum information processing, quantum interconnects and quantum memories.