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 Casimir force is mostly given by the (quantum) zero-point contribution and compensates the nanoparticle's weight. In the harmonic regime, the volume-independent characteristic frequency depends linearly on Planck's constant $hbar$.