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Measurement of the Casimir force with a ferrule-top sensor

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Measurement of the Casimir force with a ferrule-top sensor

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Measurement of the Casimir force with a ferrule-top sensor

Paul Zuurbier

Supervisors:

Sven de Man

Davide Iannuzzi

Technical support:

Kier Heeck

Associated group members:

Grzegorz Gruca

Dhwajal Chavan

P.C.Caussée

L’Album du Marin

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

A phenomenon described in 1836

A likely explanation:

The two ships act like barriers

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

H.B.G.Casimir

(1909-2000)

The Casimir effect

e.m. wave = harmonic oscillator

in vacuum

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

The energy

Between the

Plates is lower

d

Closely related

to 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.

solution

If too small → F too small

Sphere and plate Casimir force

Radius ≈ 100 µm

d≈ 40 – 200 nm

F < ~4000 pN

macroscopic objects

at microscopic distance

diameter ≈ 5000·dmin

Ferrule-top force sensor fabrication

Borosilicate ferrule

2.5 x 2.5 x 7.0 mm

Laser ablation:

200 x 200 µm ridge

100 µm gap

sphere is glued on

optical fiber is inserted

and fixed with glue

hole in cantilever is closed

gold layer is sputtered

on the sensor

Interferometer

Ferrule-top

not in

use

Table-top setup design

Left: Piezo translator with gold plate (varying d)

Right: Mechanical translator with sensor + sphere

Temperature stabilized Al cylinder

Al cover (dust and convection)

Dampers

Anechoic chamber

problems and solutions: Calibration

How does one calibrate a ferrule-top force sensor?

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: Distance

How does one measure a distance

< 100 nm with ~1 nm accuracy?

With an second interferometer we

measure Δx.

At this stage we know d = Δx + d0,

but d0 is unknown.

From the electrostatic Coulomb force

we get a signal S proportional to 1/d.

From this we can fit d0.

Δx

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 a

lock-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 get

the Casimir force from channel X (in phase) and the hydrodynamic force

from channel Y (quadrature).

Hydrodynamic results

Final results

40.000 points

no free parameters

close agreement

with theory and earlier

experiments

conclusion:

the sensor is capable

of measuring Casimir

force,

article published NJP

End