Levitation of superconducting micro-rings for quantum magnetomechanics

TL;DR

This paper demonstrates that superconducting micro-rings can be levitated using magnetic fields, offering advantages like reduced mass and enhanced control, with a theoretical framework for their stability and trapping characteristics.

Contribution

It introduces a novel theoretical framework for levitating superconducting rings in magnetic fields, highlighting benefits over solid geometries and analyzing stability conditions.

Findings

Superconducting rings can be levitated with comparable forces to solid objects.

Trapped flux provides additional control over the levitation system.

Stability in all degrees of freedom requires specific structural considerations.

Abstract

Levitation of superconductors is becoming an important building block in quantum technologies, particularly in the rising field of magnetomechanics. In most of the theoretical proposals and experiments, solid geometries such as spheres are considered for the levitator. Here we demonstrate that replacing them by superconducting rings brings two important advantages: Firstly, the forces acting on the ring remain comparable to those expected for solid objects, while the mass of the superconductor is greatly reduced. In turn, this reduction increases the achievable trap frequency. Secondly, the flux trapped in the ring by in-field cooling yields an additional degree of control for the system. We construct a general theoretical framework with which we obtain analytical formulations for a superconducting ring levitating in an anti-Helmholtz quadrupole field and a dipole field, for both zero-field and in-field cooling. The positions and the trapping frequencies of the levitated rings are analytically found as a function of the parameters of the system and the field applied during the cooling process. Unlike what is commonly observed in bulk superconductors, lateral and rotational stability are not granted for this idealized geometry. We therefore discuss the requirements for simple superconducting structures to achieve stability in all degrees of freedom.