Magnetic field fluctuations induced decoherence of a diamagnetic nanosphere

This paper provides a simple derivation of the decoherence rate for a diamagnetic nanoparticle in the presence of fluctuations of the magnetic field in a thermal environment. Diamagnetic levitation is one of the key techniques for trapping, cooling, and creating a macroscopic quantum spatial superposition in many experiments. It is widely applied in many theoretical and experimental endeavours to test fundamental physics in matter-wave interferometers. To estimate the decoherence rate originating from magnetic-field fluctuations, we use the fluctuation-dissipation theorem. We show that our resulting decoherence rate expression is analogous to that of a dielectric material interacting with the electric field component of the background field; however, it is often relatively suppressed due to the material properties.