arXiv subjects

Joachim Hofer

Publications and source records attributed to Joachim Hofer.

5 recordsLinked to original sources

arXiv2024

Remote sensing of a levitated superconductor with a flux-tunable microwave cavity

We present a cavity-electromechanical system comprising a superconducting quantum interference device which is embedded in a microwave resonator and coupled via a pick-up 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 $10^{-7} \, \mathrm{m} / \sqrt{\mathrm{Hz}}$, defines a path towards ground-state cooling of levitated particles with Planck-scale masses at millikelvin environment temperatures.

quant-ph↗

arXiv2024

A numerical approach to levitated superconductors and its application to a superconducting cylinder in a quadrupole field

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 superconductors 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 as supplemental material and can easily be adapted to various geometries and trap fields.

cond-mat.supr-con↗

arXiv2023

High-Q magnetic levitation and control of superconducting microspheres at millikelvin temperatures

We report the levitation of a superconducting lead-tin sphere with 100 micrometer diameter (corresponding to a mass of 5.6 micrograms) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240 hertz. 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 2.6e7. We also demonstrate 3D magnetic feedback control of the sphere's motion. The setup is housed in a dilution refrigerator operating at 15 millikelvin. By implementing a cryogenic vibration isolation system we can attenuate environmental vibrations at 200 hertz by approximately seven orders of magnitude. The combination of low temperature, large mass and high quality factor as well as adjustable resonance frequencies provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times.

quant-ph↗

arXiv2020

Chip-based superconducting traps for levitation of micrometer-sized particles in the Meissner state

We present a detailed analysis of two chip-based superconducting trap architectures capable of levitating micrometer-sized superconducting particles in the Meissner state. These architectures are suitable for performing novel quantum experiments with more massive particles or for force and acceleration sensors of unprecedented sensitivity. We focus in our work on a chip-based anti-Helmholtz coil-type trap (AHC) and a planar double-loop (DLP) trap. We demonstrate their fabrication from superconducting Nb films and the fabrication of superconducting particles from Nb or Pb. We apply finite element modeling (FEM) to analyze these two trap architectures in detail with respect to trap stability and frequency. Crucially, in FEM we account for the complete three-dimensional geometry of the traps, finite magnetic field penetration into the levitated superconducting particle, demagnetizing effects, and flux quantization. We can, thus, analyze trap properties beyond assumptions made in analytical models. We find that realistic AHC traps yield trap frequencies well above 10kHz for levitation of micrometer-sized particles and can be fabricated with a three-layer process, while DL traps enable trap frequencies below 1kHz and are simpler to fabricate in a single-layer process. Our numerical results guide future experiments aiming at levitating micrometer-sized particles in the Meissner state with chip-based superconducting traps. The modeling we use is also applicable in other scenarios using superconductors in the Meissner state, such as for designing superconducting magnetic shields or for calculating filling factors in superconducting resonators.

physics.app-ph↗

arXiv2018

Analytic solutions to the Maxwell-London equations and levitation force for a superconducting sphere in a quadrupole field

Recent proposals suggest using magnetically trapped superconducting spheres in the Meissner state to create low-loss mechanical oscillators with long coherence times. In these proposals the derivation of the force on the superconducting sphere and the coupling to the sphere typically relies on a vanishing penetration depth $λ$ as well as a specific symmetry (i.e. restricting the position of the sphere to one axis) or heuristic methods (e.g. assigning an equivalent point magnetic dipole moment to the sphere). In this paper we analytically solve the Maxwell-London equations with appropriate boundary conditions for a superconducting sphere in a quadrupole field. The analytic solutions provide the full field distribution for arbitrary $λ$ and for an arbitrary sphere position as well as the distribution of shielding currents within the sphere. We furthermore calculate the force acting on the sphere and the maximum field over the volume of the sphere. We show that for a certain range of $λ$ the maximum field experienced by the superconducting sphere is actually lower than it is for a non-magnetic sphere.

cond-mat.supr-con↗