Casimir nanoparticle levitation in vacuum with broadband perfect magnetic conductor metamaterials

The levitation of nanoparticles is essential in various branches of research. Casimir forces are natural candidates to tackle it but the lack of broadband metamaterials precluded repulsive forces in vacuum. We show sub-micron nanoparticle levitation in vacuum only based on the design of a broadband metamaterial perfect magnetic conductor surface, where the force is mostly given by the (quantum) zero-point contribution. In the harmonic regime of the center of mass dynamics, the characteristic frequency depends linearly on Planck's constant $\hbar$ while independent of the nanoparticle's volume.