Casimir effect in a superconducting cavity and the thermal controversy

One of the most important and still unresolved problems in the field of dispersion forces, is that of determining the influence of temperature on the Casimir force between two metallic plates. While alternative theoretical approaches lead to contradictory predictions for the magnitude of the effect, no experiment has yet detected the thermal correction to the Casimir force. In this paper we show that a superconducting cavity provides a new opportunity to investigate the problem of the thermal dependence of the Casimir force in real materials, by looking at the change of the Casimir force determined by a small change of temperature. The actual feasibility of the proposed scheme is briefly discussed.

Figure 1

Plots of $\Delta P{\phantom{\mid }\left(\mathrm{Nb}\text{−}\mathrm{Nb}\right)\mid }_{\mathrm{Dr}}$ (solid line) and $\Delta P{\phantom{\mid }\left(\mathrm{Nb}\text{−}\mathrm{Au}\right)\mid }_{\mathrm{Dr}}$ (dashed line) (in mPa) for two parallel plates at fixed separation $a=150\mathrm{nm}$, versus temperature $T_1$ (in K), for fixed $T_2\simeq T_c$.

Figure 2

Plots of $\Delta P{\phantom{\mid }\left(\mathrm{Nb}\text{−}\mathrm{Nb}\right)\mid }_{\mathrm{Dr}}$ (solid line) and $\Delta P{\phantom{\mid }\left(\mathrm{Nb}\text{−}\mathrm{Au}\right)\mid }_{\mathrm{Dr}}$ (dashed line) (in mPa) for two parallel plates versus separation $a$ (in microns), for $T_1=5\mathrm{K}$ and $T_2\simeq T_c$.

Figure 3

Plots of $\Delta F_{\mathrm{sp}}{\phantom{\mid }\left(\mathrm{Nb}\text{−}\mathrm{Nb}\right)\mid }_{\mathrm{Dr}}∕R$ (solid line) and $\Delta F_{\mathrm{sp}}{\phantom{\mid }\left(\mathrm{Nb}\text{−}\mathrm{Au}\right)\mid }_{\mathrm{Dr}}∕R$ (dashed line), in units of ${10}^{-10}\mathrm{N}∕\mathrm{m}$, versus $T_1$ (in K), for $T_2\simeq T_c$ and for fixed sphere-plate separation $a=150\mathrm{nm}$.

Figure 4

Plot of $\Delta F_{\mathrm{sp}}{\phantom{\mid }\left(\mathrm{Nb}\text{−}\mathrm{Nb}\right)\mid }_{\mathrm{Dr}}∕R$ (solid line) and $\Delta F_{\mathrm{sp}}{\phantom{\mid }\left(\mathrm{Nb}\text{−}\mathrm{Au}\right)\mid }_{\mathrm{Dr}}∕R$ (dashed line), in units of ${10}^{-10}\mathrm{N}∕\mathrm{m}$, versus sphere-plate separation $a$ (in microns), for $T_1=5\mathrm{K}$ and $T_2\simeq T_c$.