Superconducting microsphere magnetically levitated in an anharmonic potential

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 160Hz 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.