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Applied Physics Express

Damped oscillation of a magnetically-trapped superconducting micro-particle in superfluid helium: measurement of viscosity based on a hydrodynamic analysis

Shota Sasaki, Jun Naoi, Masato Takamune, Daisei Kondo, Yuta Takahashi, M. Kumakura, Masaaki Ashida, Yoshiki Moriwaki

Published Jul 11, 2023• 0 citations
Publisher

Abstract

Abstract We have developed a trap of a single superconducting micro-particle using a quadrupole magnetic field in superfluid helium. By displacing the particle from a stable static position and then releasing it, the particle was observed to oscillate around the stable position. Analyzing the damped oscillation, we have demonstrated the measurement of the viscosity of superfluid helium.

DOI
10.35848/1882-0786/ace679

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Abstract We have developed a trap of a single superconducting micro-particle using a quadrupole magnetic field in superfluid helium. By displacing the particle from a stable static position and then releasing it, the particle was observed to oscillate around the stable position. Analyzing the damped oscillation, we have demonstrated the measurement of the viscosity of superfluid helium.
Superfluid helium is an important model system to study quantum hydrodynamics. Numerous researches have been reported on fascinating phenomena including superfluidity, unusually low viscosity, and the emergence of the quantum vortex. Here, we demonstrated the visualization of the quantum vortices, which are intrinsically unable to be seen. We prepared many nanoparticles in superfluid helium by using the laser ablation technique. The fabricated nanoparticles are trapped at the core of the quantum vortices. By imaging the scattered light from the nanoparticles, we visualized the motion of the quantum vortices.
At finite temperature, the hydrodynamic collective modes of superfluid trapped Fermi gases are coupled to the motion of the normal component, which in the BCS limit behaves like a collisionless normal Fermi gas. The coupling between the superfluid and the normal components is treated in the framework of a semiclassical transport theory for the quasiparticle-distribution function, combined with a hydrodynamic equation for the collective motion of the superfluid component. We develop a numerical test-particle method for solving these equations in the linear-response regime. As a first application we study the temperature dependence of the collective quadrupole mode of a Fermi gas in a spherical trap. The coupling between the superfluid collective motion and the quasiparticles leads to a rather strong damping of the hydrodynamic mode already at very low temperatures. At higher temperatures the spectrum has a two-peak structure, the second peak corresponding to the quadrupole mode in the normal phase.
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.
Abstract Magnetically levitated superconductors in the Meissner state can be utilized as micro-mechanical oscillators with large mass, high quality factors and long coherence times. In previous works analytical solutions for the magnetic field distribution around a superconducting sphere in a quadrupole field have been found and used to derive the trap parameters, while non-spherical geometries have only been investigated in a few idealized cases. However, superconductors of almost arbitrary shape can be used as levitators in a magnetic trap and, as the trap’s properties depend strongly on the superconductor’s shape, allow for a wider parameter regime to be accessed. Finite element models are suitable to obtain the field distribution around arbitrarily shaped superconductors in arbitrary fields, but have not yet been used widely in the context of levitated superconductors. Here we present a simple numerical model for this purpose and use it to calculate the field distribution around cylindrical superconductors in a quadrupole field and to evaluate the trap parameters. We find that the cylindrical shape, compared to spherical levitators, allows for substantially higher trap frequencies and coupling strengths. This in turn reduces the demands on vibration isolation and significantly eases the requirements for feedback cooling to the ground state. The numerical model is provided in a file repository and can easily be adapted to various geometries and trap fields.
Turbulence enhances momentum transport in classical fluids, effectively increasing their viscosity. We investigate an analogous effect in a superfluid by measuring the damping of collective oscillations in an atomic Bose-Einstein condensate (BEC) containing stationary spin-superflow turbulence. Using continuous spin driving to maintain turbulence in a spin-1 ^{23}Na BEC, we excite its quadrupole mode and measure the damping rate over a range of temperatures. The damping consistently exceeds the Landau-damping rate expected for an equilibrium, nonturbulent BEC. The enhancement likely originates from two complementary processes: direct energy transfer from the mode to turbulent condensate fluctuations and turbulence-induced modification of the thermal cloud that amplifies Landau damping. These results establish collective-mode damping as a sensitive probe of momentum transport in superfluid turbulence.