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

A phenomenon described in 1836 P.C.Caussée L’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 ( ) d 1948: In the presence of two parallel plates (conductors) e.m. wave = harmonic oscillator in vacuum The energy Between the Plates is lower 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.

Sphere and plate Casimir force  solution If too small → F too small Radius ≈ 100 µm d ≈ 40 – 200 nm F < ~4000 pN macroscopic objects at microscopic distance diameter ≈ 5000·d min

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

not in use 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 d 0. With an second interferometer we measure Δx. At this stage we know d = Δx + d 0, but d 0 is unknown. ΔxΔx

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 points no free parameters close agreement with theory and earlier experiments conclusion: the sensor is capable of measuring Casimir force, article published NJP

End