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

Abstract

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 (DL) 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 10 kHz for levitation of micrometer-sized particles and can be fabricated with a three-layer process, while DL traps enable trap frequencies below 1 kHz 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.

A Chip-Based Superconducting Magnetic Trap for Levitating Superconducting Microparticles

“…2), magnetic force and supercurrents. We assume that the particle is in the Meissner state and model it via the Maxwell-London equations in A-V formulation [24]. This situation holds when the particle is cooled below its critical temperature in zero field, and if the field near the particle stays below the first critical field of the material that the particle is made of, as is the case in our experiment.…”

“…In order to stably levitate a diamagnetic particle, first, a three-dimensional magnetic field minimum is required to confine it [24], [26]. The magnetic field distribution used to achieve such a confinement resembles that of an anti-Helmholtz coil configuration.…”

“…To simulate the particle in the trap, we account for the three-dimensional geometry of the coils and the particle. We do this because the sample is not symmetric, thus, planar or rotationally symmetric twodimensional models fail to capture its behavior, and also because the particle perturbs the trap field due to field expulsion [23], [24], [31]. We calculate the magnetic field distribution from finite element method simulations using COMSOL Multiphysics [32].…”

“…The simulations operate in the static regime and are based on the A-V formulation of the Maxwell-London equations [33], for details see Ref. [24]. The simulations yield the magnetic field (shown in Fig.…”

“…The simulated magnetic field allows us to estimate the trapped particle's centre-of-mass (COM) motional frequencies: We calculate the restoring force acting on the particle when it is shifted by a small distance from its equilibrium position [24]. In this way, we obtain motional frequencies for a 50 µm particle, (ω x , ω y , ω z ) = 2π × (43 ± 4, 64 ± 19, 125 ± 3) Hz when 0.5 A current is passed through the coils (error is simulation uncertainty, see Ref.…”