Superconducting flux concentrator coils for levitation of particles in the Meissner state

Magnetic levitation of superconductors is a promising platform to study quantum mechanics in the large-mass limit. One major limitation is the weak trapping potential, which results in low vibrational eigenfrequencies and increased susceptibility to low-frequency noise. While generating strong magnetic fields is relatively straightforward, creating a tightly confined harmonic potential-essentially achieving a large magnetic field gradient-remains a significant challenge. In this work, we demonstrate a potential solution using superconducting cores that concentrate magnetic flux into arbitrarily small volumes. We show the ability to trap superconducting particles using an anti-Helmholtz coil configuration incorporating these cores. However, we observe rapid damping of the levitated particle motion due to flux trapping within the cores, occurring once the lower critical field is exceeded locally. To investigate this mechanism, we employ diamond nitrogen-vacancy center magnetometry and detect substantial remanent fields persisting after high-current operation of the coils. Finally, we discuss possible strategies to mitigate this effect and improve the levitation properties.