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Magnetically levitated superconducting microparticles offer a promising path to quantum experiments with picogram to microgram objects. In this work, we levitate a 700ng $\sim 10^{17}$amu superconducting microsphere in a magnetic chip trap in which detection is integrated. We measure the particle's center-of-mass motion using a DC-SQUID magnetometer. The trap frequencies are continuously tunable between 30 and 160 Hz and the particle remains stably trapped over days in a dilution refrigerator environment. We characterize motional-amplitude-dependent frequency shifts, which arise from trap anharmonicities, namely Duffing nonlinearities and mode couplings. We explain this nonlinear behavior using finite element modelling of the chip-based trap potential. This work constitutes a first step towards quantum experiments and ultrasensitive inertial sensors with magnetically levitated superconducting microparticles., Comment: version close to published version; 16 pages, 13 figures

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$\,\mu$m to 200$\,\mu$m. 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 50\,$\mu$m diameter SnPb microparticle at temperatures of 4\,K and 40\,mK., Comment: 6 pages, 6 figures, video material available at https://doi.org/10.5281/zenodo.5911190

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., Comment: close to published version, 16 pages, 19 figures

We perform an experimental and numerical study of dielectric loss in superconducting microwave resonators at low temperature. Dielectric loss, due to two-level systems, is a limiting factor in several applications, e.g. superconducting qubits, Josephson parametric amplifiers, microwave kinetic-inductance detectors, and superconducting single-photon detectors. Our devices are made of disordered NbN, which, due to magnetic-field penetration, necessitates 3D finite-element simulation of the Maxwell--London equations at microwave frequencies to accurately model the current density and electric field distribution. From the field distribution, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. We emphasise that the loss caused by a spin-on-glass resist such as hydrogen silsesquioxane (HSQ), used for ultrahigh lithographic resolution relevant to the fabrication of nanowires, and find that, when used, HSQ is the dominant source of loss, with a loss tangent of $\delta^i_{HSQ} = 8 \times 10^{-3}$.