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.
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Measurement of the Casimir force with a ferrule-top sensor
Sven de Man
Associated group members:
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”
The Casimir effect
e.m. wave = harmonic oscillator
1948: In the presence of two parallel plates (conductors)
Plates is lower
to van der
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.
Test the new sensor by performing the first
ferrule-top Casimir force measurement.
If too small → F too small
Sphere and plate Casimir force
Radius ≈ 100 µm
d≈ 40 – 200 nm
F < ~4000 pN
at microscopic distance
diameter ≈ 5000·dmin
Ferrule-top force sensor fabrication
2.5 x 2.5 x 7.0 mm
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
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)
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
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.
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
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).
no free parameters
with theory and earlier
the sensor is capable
of measuring Casimir
article published NJP