Thermal fluctuations and stability of a particle levitated by a repulsive Casimir force in a liquid

We study the vertical Brownian motion of a gold particle levitated by a repulsive Casimir force to a silica plate immersed in bromobenzene. The time evolution of the particle distribution starting from an equilibrium position, where the Casimir force and gravitational force are balanced, is considered by solving the Langevin equation using the Monte Carlo method. When the gold particle is very close to the silica plate, the Casimir force changes from repulsive to attractive, and the particle eventually sticks to the surface. The escape rate from a metastable position is calculated by solving the Fokker-Plank equation; it agrees with the value obtained by Kramers' escape theory. The duration of levitation increases as the particle radius increases up to around 2.3 μm. As an example, we show that a 1-μm-diameter gold particle can be levitated for a significantly long time by the repulsive Casimir force at room temperature.