Repulsive Casimir force in magnetodielectric plate configurations

The Casimir force between purely dielectric materials is generally attractive and can lead to increased friction and stiction effects in nanoscale devices. While prospective quantum levitating systems have been proposed for high dielectric constant host materials, reversal of the Casimir force with air/vacuum as the intermediate medium remains challenging. Here, the problem of quantum levitation is studied for a system consisting of two parallel magnetodielectric plates. A simple analytical treatment of the problem is provided through the introduction of an upper bound of the force. An explicit sufficient condition for the manifestation of Casimir force repulsion is derived in terms of the plate's material parameters and temperature. The sufficient condition can serve as a useful tool in designing quantum levitating systems with air as the intermediate medium, which is the natural environment for practical microscopic devices.

Figure 1

(a) The Casimir force (solid lines) and its upper bound (dashed lines) calculated for two ratios of the plate 2 dielectric and magnetic plasma frequencies ${\omega }_{pe2}/{\omega }_{pm2}$ and fixed ${\omega }_{0m2}/{\omega }_T=1$. (b) The temperature dependence of the force and its upper bound is calculated for different temperatures with fixed plasma and resonance frequencies ${\omega }_{pe2}/{\omega }_{pm2}=0.25$, ${\omega }_{0e2}/{\omega }_{0m2}=2$, and ${\omega }_{pm2}/{\omega }_{0m2}=0.5$. The large distance $F_{\infty }$ and the small distance $F_0$ asymptotics are included and in all calculations we have set the plate 1 permittivity at ${\varepsilon }_1=2$.

Figure 2

(a) Repulsive Casimir force domain according to Eq. (13) (region $A$, blue) and Eq. (11) (region $B$, gray). (b) The range of plate separation distances for force repulsion is calculated at fixed ${\omega }_{0m2}/{\omega }_T=1$ and ${\omega }_{pe2}/{\omega }_{pm2}={\omega }_{pm2}/{\omega }_{0m2}=0.5$. The dots correspond to the parametric domain for force reversal obtained through exact numerical solutions of the actual force given by Eq. (6). In all cases, we have set the plate 1 permittivity at ${\varepsilon }_1=2$.

Figure 3

Quantum levitation in magnetodielectric plate configurations. (a) The complete parametric domain for Casimir force reversal according to the sufficient condition Eq. (16). (b) The parametric domain represented by the optical constants described Lorentz oscillator model with ${\omega }_{pm2}/{\omega }_{0m2}=0.5$. In all cases, we have set the plate 1 permittivity as ${\varepsilon }_1=2$.

Figure 4

A comparison between the repulsive Casimir force domains calculated based on the sufficient condition Eq. (15) (blue domain) and through exact numerical integration of Eq. (6) (dots). In the calculations, we vary the compound parameters and have fixed (a) ${\omega }_{pe2}/{\omega }_{pm2}=0.9$ and ${\omega }_{pm2}/{\omega }_{0m2}=0.5$, and (b) ${\omega }_{0m2}/{\omega }_T=0.5$ and ${\omega }_{pe2}/{\omega }_{pm2}=0.1$. In all cases, we have set the plate 1 permittivity as ${\varepsilon }_1=2$.