Repulsive Casimir-Polder forces on a magnetic particle
We explore the feasibility of realizing repulsive Casimir-Polder (CP) forces for a magnetic particle near a surface. Considering the toy model of an atom with an electric-dipole transition and an arbitrarily large magnetic spin, we analyze the interplay between the repulsive magnetic-dipole and the attractive electric-dipole contributions to the total CP force. Particularly noting that the magnetic CP interaction is relatively longer-ranged than the electric CP interaction due to the difference in their respective characteristic transition frequencies, we find a regime where the repulsive magnetic contribution to the total force can potentially exceed the attractive electric part in magnitude, thus making the overall force repulsive. We discuss some fundamental constraints and conditions necessary for achieving such a repulsion, identifying the magnetizability to polarizability ratio for the particle as a key figure of merit. We analyze ways to further enhance the magnitude of the repulsive magnetic CP force for an excited magnetic atom, such as, by preparing the atom in a ``super-radiant'' magnetic sub-level, and designing surface resonances close to the magnetic transition frequency. Our results could be instructive in identifying potential systems, mechanisms, and regimes where one could realize stable levitation via repulsive magnetic Casimir-Polder forces.