Demonstration of the Difference in the Casimir Force for Samples with Different Charge-Carrier Densities

A measurement of the Casimir force between a gold coated sphere and two Si plates of different carrier densities is performed using a high vacuum based atomic force microscope. The results are compared with the Lifshitz theory and good agreement is found. Our experiment demonstrates that by changing the carrier density of the semiconductor plate by several orders of magnitude it is possible to modify the Casimir interaction. This result may find applications in nanotechnology.

Figure 1

The data of the mean measured Casimir force as a function of separation between a gold coated sphere and two Si plates of ($a$) higher and ($b$) lower resistivities are shown as dots.

Figure 2

Dielectric permittivities along the imaginary frequency axis for gold (solid line) and for Si (dashed lines $a$ and $b$ are for higher and lower resistivity Si, respectively).

Figure 3

Differences of the theoretical and mean experimental Casimir forces versus separation. Forces are computed and measured for ($a$) higher and ($b$) lower resistivity Si. Solid lines indicate 95% confidence intervals.

Figure 4

The differences of the mean measured Casimir forces of the lower and higher resistivity Si samples versus separation are shown as dots. The corresponding theoretically calculated differences are shown by the solid line.