Measurement of the Casimir force with a ferrule-top sensor

Paul Zuurbier

Supervisors:Sven de ManDavide Iannuzzi

Technical support:Kier Heeck

Associated group members:Grzegorz GrucaDhwajal Chavan

A phenomenon described in 1836

P.C.CausséeL’Album du Marin

Two parallel ships are driven to each other by a mysterious attractive force

They are pushed one against the other by the waves outside “the gap”

A likely explanation:The two ships act like barriers

The Casimir effect

H.B.G.Casimir(1909-2000)

d

1948: In the presence of two parallel plates (conductors)

e.m. wave = harmonic oscillator

in vacuum

0 2

1dE

The energyBetween thePlates is lower

CasimirF

Closely relatedto van der Waals force

The need of ferrule-top Casimir measurement

Increasing 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.

Sphere and plate Casimir force

solution

If too small → F too small

Radius ≈ 100 µm

d ≈ 40 – 200 nm

F < ~4000 pN

macroscopic objectsat microscopic distancediameter ≈ 5000·dmin

Ferrule-top force sensor fabrication

Borosilicate ferrule2.5 x 2.5 x 7.0 mm

Laser ablation:200 x 200 µm ridge

100 µm gap

sphere is glued on

optical fiber is insertedand fixed with glue

hole in cantilever is closed

gold layer is sputteredon the sensor

not inuse

Ferrule-top

Interferometer

Temperature stabilized Al cylinder

Al cover (dust and convection)

Dampers

Table-top setup design

Left: Piezo translator with gold plate (varying d)

Right: Mechanical translator with sensor + sphere

Anechoic chamber

We 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?

problems 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 Δx. At this stage we know d = Δx + d0,but d0 is unknown.

Δx

nmd

pNF

d

F

7

500

problems and solutions: Noise and drift

Since k~7 N/m and F<4 nN the cantilever bends only half a nanometer!

In this situation the drift of the interferometer intensity is overwhelming.Therefore we vibrate the plate and measure ΔF:

Because we are modulating the Casimir force we can use alock-in amplifier with superior noise suppression (AM).

problems and solutions: Hydrodynamics

Plate vibration airflow hydrodynamic force on sphere.

How does one distinguish between hydrodynamic and Casimir force?

The Casimir force depends on d ~ cos(ωt)

The hydrodynamic force depends on ~ -sin(ωt)

Both signals are 90° out of phase (orthogonal).

The signal is measured with a lock-in amplifier and we can getthe Casimir force from channel X (in phase) and the hydrodynamic forcefrom channel Y (quadrature).

t

d

Hydrodynamic results

Final results

40.000 points

no free parameters

close agreementwith theory and earlierexperiments

conclusion:the sensor is capableof measuring Casimirforce,article published NJP

End