Title : Stabilizing levitation of a graphene flake in a magnetic field through the Casimir effect
Abstract:
To probe the fundamental quantum mechanical aspects of mesoscopic objects, the phenomenon of quantum decoherence must be effectively mitigated. A primary pathway for decoherence involves the object's physical contact with its environment; consequently, non-contact levitation offers a promising route to maintaining quantum coherence. While optical trapping has been successfully employed for levitating atomic and molecular species, its application is generally unavailable for nanoscale objects such as graphene flakes.
In this work, we propose and analyze a novel levitation scheme specifically designed for a graphene flake, integrating the effects of diamagnetism and the Casimir force. Graphene exhibits robust diamagnetism, enabling it to be levitated above a suitable magnetic field source. However, the strong anisotropy of its magnetic permeability poses a significant challenge to stable levitation. The permeability of a graphene sheet is substantially greater perpendicular to its surface than parallel to it . This anisotropy generates a magnetic torque that forces the flake to rotate until its surface is oriented parallel to the magnetic field lines. To achieve stable levitation where the flake's orientation can be maintained at a desired angle, a counteracting, stabilizing torque is required to oppose this rotational tendency.
We demonstrate that the Casimir effect provides the necessary stabilizing torque. The quantum vacuum's electromagnetic field between the graphene flake and the magnet's surface is confinement-dependent, meaning it changes as a function of the flake's rotation angle. As a result, the Casimir energy—the renormalized summation of the zero-point energy between the flake and the magnet's surface—varies with orientation. The minimum Casimir energy is achieved when the graphene flake is positioned parallel to the surface of the magnet. Thus, this interaction inherently generates a restoring torque that favours the parallel orientation.
The ultimate stability of the levitated graphene flake is therefore governed by the delicate balance and interplay between the destabilizing magnetic torque and the stabilizing Casimir torque. We present a detailed analysis of the Casimir torque's dependence on the levitation height. Our findings conclusively show that the Casimir effect provides a mechanism to stabilize the diamagnetic levitation of a graphene flake, offering a viable path toward utilizing such nano-objects for macroscopic quantum experiments.
