Coupling a Flux-Tunable Resonator to a Magnetically Levitated Superconducting Microparticle

Doktorsavhandling, 2026

Magnetically levitated superconducting microparticles provide a promising platform for fundamental quantum experiments and quantum-limited sensing. In the Meissner state, the levitated particle is trapped without mechanical clamping, allowing its center-of-mass motion to exhibit ultralow dissipation. The particle's displacement can be read out dispersively via magnetic flux coupling to superconducting resonators. A challenge for magnetomechanical coupling is to realize a flux-tunable microwave circuit that provides strong flux-to-frequency transduction, low dissipation, and a sufficiently large linear operating range for readout and cooling. This thesis develops and characterizes a chip-based superconducting platform for realizing this transduction.

Chip-based levitation of a superconducting microparticle is demonstrated at 40 mK. Passive cryogenic vibration isolation is developed to increase the mechanical quality factors of the levitated particle. For coupling to a microwave circuit, a superconducting flip-chip process based on indium microspheres was developed. The need for Au passivation of Nb or NbN under-bump metallization is demonstrated, and indium-based superconducting interconnects are shown to carry ampere-scale currents. Flux-tunable resonators with 100-200 µm SQUID loops and integrated input coils are designed, fabricated, and characterized. A peak flux responsivity of 20 GHz/Φ₀ is achieved, with one flux quantum modulation requiring only 10-20 µA of input-coil current. Two integrated flux-biasing architectures are developed with flip-chip and on-chip input coils, achieving a total flux transfer efficiency of 1.6%. Junction asymmetry is shown to suppress branch-switching behavior associated with finite SQUID screening.

Together, these results establish the superconducting subsystems required for dispersive microwave readout of the center-of-mass motion of a levitated microparticle. Such a magnetomechanical coupling provides a route toward cooling the center-of-mass motion to the ground state, paving the way for the preparation of nonclassical motional states. More broadly, such systems are well-suited for quantum-limited force and acceleration sensing, as well as for probing quantum physics in a previously unexplored mass regime.