Casimir Force Measurements
(Hedwig Eerkens, Sven de Man, Dirk Bouwmeester)

spheres Photograph (left) and SEM image (right) of the microscopic sphere attached to an AFM cantilever. The polystyrene sphere has a diameter of 100 micrometer and is coated with a 200 nanometer thick gold layer.

 

In 1948 Casimir predicted that two parallel, perfectly conducting plates in vacuum experience an attractive force. His theory was later expanded by Lifshitz to the case of real conductors. But applying this theory requires full knowledge of the material's dielectric function, which is difficult to obtain. It is not possible to measure the dielectric function at all frequencies and it is unclear what theoretical model is suitable to extend the experimental data to the full frequency domain. It is therefore necessary to measure the Casimir force for different materials in order to find indications for what theoretical model is best used.

 

Difficulties also arise in measuring the Casimir force. Getting two plates perfetly parallel is already a challenge. Therefore we use a setup similar to an atomic force microscope (AFM), where we measure the force between a flat plate and a microscopic sphere attached to an AFM-type cantilever. However, the Casimir force is not the only force acting on the sphere. There is a bigger contribution from the electrostatic force caused by a difference in surface potential. The size of this contribution is unknown and difficult to separate from the contribution of the Casimir force, since both forces result in a static deflection of the cantilever.

 

We overcome this issue by modulating the electrostatic force, thereby separating its contribution in frequency space. The dynamic deflection of the cantilever can now be used to calibrate the electrostatic force. This modulation trick can simultaneously be used to overcome another issue. It allows us to calibrate the distance between the sphere and the plate, which would otherwise be hard to determine reliably.

 

In our research we combine this modulation technique with the Leiden expertise in cryogenic techniques. We can therefore measure the Casimir force at liquid helium or even at milliKelvin temperatures. This unique setup allows us to increase our knowledge of the Casimir force not only by the extended temperature range, but also by the possiblity to measure the force between superconductors.

 

spheres Schematic image of the setup. The force between the superconducting plate and gold sphere causes the cantilever to deflect. This deflection is picked up via fiber interferometry and different elements of this signal can be used to calibrate the setup.