Slide 1

Measurement of the Casimir force with a ferrule-top sensorPaul Zuurbier

Supervisors:Sven de ManDavide Iannuzzi

Technical support:Kier Heeck

Associated group members:Grzegorz GrucaDhwajal Chavan

1A phenomenon described in 1836

P.C.CausseLAlbum du MarinTwo parallel ships are driven to each other by a mysterious attractive forceThey are pushed one against the other by the waves outside the gapA likely explanation:The two ships act like barriers2

The Casimir effect

H.B.G.Casimir(1909-2000)d1948: In the presence of two parallel plates (conductors)

e.m. wave = harmonic oscillator

in vacuum

The energyBetween thePlates is lower

Closely relatedto van der Waals forceWithout any EM-sources the quantum number n=0At the surface of the plates E=0Closely related with van der Waals-force -> kleine afstanden3The need of ferrule-top Casimir measurementIncreasing interest in studying the Casimir force in various environments, for instance in liquids and with varying temperature.Our group designed and manufactured the ferrule-top sensor, which is versatile, adaptive and cost effective:

Measuring Casimir force is difficult, so it is a good benchmark.My job: Test the new sensor by performing the first ferrule-top Casimir force measurement.4Sphere and plate Casimir forcesolution

If too small F too small

Radius 100 md 40 200 nmF < ~4000 pN

macroscopic objectsat microscopic distancediameter 5000dmin5Ferrule-top force sensor fabrication

Borosilicate ferrule2.5 x 2.5 x 7.0 mm

Laser ablation:200 x 200 m ridge

100 m gap

sphere is glued on

optical fiber is insertedand fixed with glue

hole in cantilever is closedgold layer is sputteredon the sensor6

not inuseFerrule-top

Interferometer7

Temperature stabilized Al cylinderAl cover (dust and convection)

DampersTable-top setup design

Left: Piezo translator with gold plate (varying d)

Right: Mechanical translator with sensor + sphereAnechoic chamber

Storyline: We need to measure F(d) for very short d and large objects8We calibrate continuously by applying a well known electrostatic force.

We apply an AC voltage to the sphere

We measure the signal due to this force

at double the frequency

We calculate the sensitivity problems and solutions: Calibration

How does one calibrate a ferrule-top force sensor?

Reference to TL9problems and solutions: Distance

How does one measure a distance< 100 nm with ~1 nm accuracy?From the electrostatic Coulomb force

we get a signal S proportional to 1/d. From this we can fit d0.

With an second interferometer we measure x. At this stage we know d = x + d0,but d0 is unknown.

x10

problems and solutions: Noise and driftSince k~7 N/m and F