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arXiv:2211.06289 · Physical Review Letters

High- Q Magnetic Levitation and Control of Superconducting Microspheres at Millikelvin Temperatures

Joachim Hofer, R. Gross, Gerard T. Higgins, Hans Huebl, Oliver Kieler, R. Kleiner, D. Koelle, Philip Schmidt, Joshua A. Slater, Michael Trupke, Kevin Uhl, Thomas Weimann, Witlef Wieczorek, Markus Aspelmeyer

Published Jul 25, 2023• 57 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.131.043603

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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.
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.
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 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.
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 show that by magnetically trapping a superconducting microsphere close to a quantum circuit, it is possible to perform ground-state cooling and prepare quantum superpositions of the center-of-mass motion of the microsphere. Due to the absence of clamping losses and time-dependent electromagnetic fields, the mechanical motion of micrometer-sized metallic spheres in the Meissner state is predicted to be very well isolated from the environment. Hence, we propose to combine the technology of magnetic microtraps and superconducting qubits to bring relatively large objects to the quantum regime.