Development of a high-sensitivity torsion balance to study the thermal Casimir force

(and more..)Woo-Joong Andy Kim

Sept 22, 2011Department of Physics

Seattle University

It all starts from a simple idea

Casimir Force

• Macroscopic effects of quantum fluctuations

• Scaling law distinct from the gravitational and electric forces

• Retarded van der Waals interaction at large separations.

• The force can be re-derived from the Lifshitz formula.

Force-distance measurements

• Simple force-distance measurements using an AFM or a torsion balance• Two metal plates facing each other and brought closer to separations down to submicron meter. • Due to experimental difficulty with parallelism, a sphere-plane configuration is often employed.

• What are distinct types of interaction forces one can expect to observe from a measurement?

✔ ✔

• Exists despite that the electric forces are minimized with contact potentials may not be completely nullified [1].

Patch force (Fpatch)

[1] W. J. Kim and U. D. Schwarz, J. Vac. Sci and Tech. B 28 C4A1 (2010). [2] W. J. Kim et al., PRL 103, 060401 (2009); PRA 81, 022505 (2010).[3] R. O. Behunin et al. arXiv: 1108.1761 (2011).[4] B. C. Stipe et al., PRL 87, 096801 (2001) N. A. Burnham et al, PRL 69, 133 (1992)[5] A. Naji et al., PRL 104, 060601 (2010).

• Must be distinguished from the actual forces of thermal and quantum fluctuations (e.g. Casimir/Lifshiz force)

• In a realistic experiment, only the sum is measured. At the minimized condition V=Vm,

• Different models of patch force have been discussed, but it is not very clear how to apply a particular model for a given experiment [3-5].

Experimental: How do we measure it?

PID controllerGenerates δV

Feedback plates

Quadrant photodetector667 nm Diode Laser

V0+δV

V0-δV

PZT actuator

Proportional-Integral-Derivative (PID) controller puts out correction voltage δV, which is proportional to a force exerted on test plates.

Pivot point

Casimir plates

Just remember..

SPID=SDC+δV

Force is directly proportional to SPID

Contains distance-dependent force, such as

Acquisition of experimental data

SPID

V0

Electrostatic calibration

Curvature analysis I

Parabola curvature analysis• Calibration factor ()• Absolute distances (d)

d0 allows to assess the absolute distance

Interesting to verify if d0 coincides with the actual distance e.g. Prof. H. B. Chan’s on-chip device.

Contact potential analysis II

Very important! Vm is not necessarily constant. In fact, it may change with distances

[1] W. J. Kim, M. Brown-Hayes, D. A. R. Dalvit, J. H. Brownell, and R. Onofrio PRA 78 020101 (R) (2008)

[2] de Man, K. Heeck, and D. Iannuzzi. PRA 79 024102 (2009); de Man, K. Heeck, R. J. Wijngaarden, and D. Iannuzzi. J. Vac. Sci and Tech. B 28 C4A25 (2010).

[3] W. J. Kim, A. O. Sushkov, D. DalvitS. K. Lamoreaux. PRL 103, 060401 (2009)

Most AFM measurements: 100-500 nm

Measured range from 100 μm to 100 nm: 3 orders of magnitude

[7] S. E. Pollack, S. Schlamminger, and J. H. Gundlach. PRL 101, 071101 (2008).

[4] G. Torricelli, I. Pirozhenko, S. Thornton, A. Lambrecht, and C. Binns. EPL 93 51001 (2011).

[5] G. Torricelli et al. PRA 82 010101 (R) (2010)

[6] Q. Wei et al., PRA 81, 052115 (2010).

Contact potential difference (CPD)

V

• A combination of work function, surface potential patches (spatially varying), charging effects, and wire connections..

• CPD cannot be measured with a voltemeter!

• Kelvin probe microscopy (KPM) can measure this. Essentially, this is a minimizing condition for a force between two plates

• Same as work function? Not really..

Naïve picture of an ideal situation

Perfectly smooth, homogeneous samples

Unique values of capacitance and contact potential

When electrostatic force is minimized, it’s always nullified

In reality..

More realistic picture of the situation

Distance-dependent contact potentials!

Electrostatic force is no longer nullified AND

It could interfere with other distance-dependent forces of great physical interest

Distance-dependent Electric force even Vm!

The situation becomes more complicated in a real experiment

Fpatch(d)

The CPD is an old problem…

[1] Bridgman. Phys. Rev 14, 306 (1919).[2] Dowling. Phys. Rev. 25, 812 (1925).[3] Dowling. Phys. Rev 31 244 (1928).[4] B. R. Rose, Phys. Rev 44 585 (1933).[5] C. W. Oately. Proc. Royal Society of London: Math and Phys. 155 218 (1936).[6] H. H. Uhlig. J. Appl. Phys. 22 1399 (1951).

Contact potential variation at different temperature/CPD between the solid and liquid phases [1-3].

Measurements on contact potential difference between faces of copper single crystals. Found CPD greater than 463 mV. “This is much great than was anticipated for a symmetrical cubic crystal and indicates desirability of extending the investigation to other crystals” [4]

Volta potentials of the Copper-Nickel alloys and several metals in air. Test of temporal stability [6]

GP-B/LISA/LIGO Patch effect being the largest systematic errors for Gravity probe B: PRL 106 221101 (2011).

Ion-trap/neutral atom exp

Physics 4, 66 (2011)http://physics.aps.org/articles/v4/66 :” All that is gold does not glitter”

[3] M. Lucchesi, G. Privitera, M. Labardi, D. Prevosto, D. Capacciloli, P. Pingue. arXiv:0901.0500 (2009) Repulsive/attractive electric force depending on CPD.

[1] F. Bocquet, L. Nony, C. Loppacher, and T. Glatzel. PRB 78 035310 (2008) short range electrostatic force/ variation of contact potential with respect to z distance as well as lateral position.

Noncontact atomic force microscopy (NC-AFM)

Review paper: W. J. Kim and U. D. Schwarz, J. Vac. Sci and Tech. B 28 C4A1 (2010)

[2] G. H. Enevoldsen, T. Glatzel, M. C. Christensen, J. V. Lauritsen, and F. Besenbacher.PRL 236104 (2008) Atomic scale surface potential variation using KPM

Fluctuation induced friction measurements (in the early 90s)

Particle physics: Freely falling electrons under the influence of gravity (in the 70s)

Distance-Dependent Forces

Casimir force due to quantum vacuum fluctuation

Coulombian force due to spatial fluctuation of patches

How do we distinguish between the two?Some critical questions we should be asking:

Could the surface effect ever be accurately and precisely taken into account in a precision force measurement?If not, could one ever observe a pure Casimir force in a realistic experiment employing a pair of real samples that necessarily bear defects and inhomogeneity to some degrees?

Do you have any suggestions?

Our experiment

Nano rotator (360 rotation)

Position-sensitivePhotodetector (PSPD)

3-axis position stagewith peltier (TEC) cooler

Pump system: DiffusionRoughing (not shown)

Schematic of our torsion balance

PID controllerGenerates δV

Feedback plates

Quadrant photodetector667 nm Diode Laser

V0+δV

V0-δV

PZT actuator

Proportional-Integral-Derivative (PID) controller puts out correction voltage δV, which is proportional to a force exerted on test plates.

Pivot point

Casimir plates F

Torsion balance

Tungsten fiber

Detection Mirror

Damping magnetc

Feedback plates (for compensation)

Casimir plates

Preliminary data for feedback control

Time (sec)

Phot

odet

ecto

r (V)

Sensitivity

Tungsten fiber d=76 μm has been etched in copper solution by electrochemistry and is now firmly held in place. The fiber length is currently set to l=20 cm.

The torsion has mass m=97.3 g, and its thermal angular fluctuations for the swinging (gravitational) pendulum mode is

Here, α is the torque coefficient similar to “spring constant” and is an intrinsic quantity for our tungsten fiber. α=2.9x10-6 N m/rad

This is much smaller than the torsional angular fluctuation, which comes from angular restoring torque given by

Based on fluctuation-dissipation theorem, the rms force noise.

The angular resolution of the photodiode is estimated to beδθ=0.5 mV/μrad. This is based on 6 mm photodiode diameter with max output voltage of 10 V at a distance of 30 cm from the detection mirror.

Conservative estimate for force resolution, if the angular tilt of 1 μrad is assumed, is about 30 pN. This is equivalent to the Casimir force at a few μm separation in a typical sphere-plane configuration.

The entire balance will be put together in vacuum inside a bell jar. Both roughing and diffusion pumps have been installed. Target pressure 10-7 torr to be achieved soon.

Construction of closed-loop PZT

Applied voltage (V)

Actu

al d

ispl

acem

ent

(arb

uni

t)

Circuit to provide feedback voltage

Michelson’s interferometer for PZT calibration

Independent PZT calibration using a He-Ne laser (632.816 nm)

Vibration isolation table (floating)

PZT sweep

Fringe changes

Full period= λ/2

Relate the period to a change in voltage applied to PZT to obtain a calibration factor. (630 nm/V)

Visibility over 90% achieved.

Research directions1. Precision electric force microscopy: (a) Look for size-dependent contact potentials, force constant, and surface patch forces at large distances. (b) Employ KPM to collect information about local patches. (c) Investigate the behavior of electrostatic scaling exponent over many order of distances.

BK quartz (cm sized) Diode lens (mm sized) Polysterine (μm sized)

10.3 cm 0.55 mm 45 μm

15.5 cm 1.10 mm 110 μm

30.9 cm 1.65 mm 380 μm

154.5 cm 2.75 mm 600 μm

2. Thermal Casimir force revisited: How do we properly separate the two contributions (Fcas & Fpatch)? Extend the measurement range to 10 μm or more

3. The Casimir force in graphene sample

Science 324 1312 (2009)

Large-area synthesis seemsfeasible now!!!

We are currently working with Dr. Daniil Stolyarov at Graphene Laboratories to deposit a thick layer of graphene flakes on Si/SiO2 substrate by polymer free method (Testing stage).

M. Bordag et al., PRB 74 205431 (2006)M. Bordag et al., PRB 80 245406 (2009)Bo. E. Sernelius EPL 95 57003 (2011)V. Svetovoy et al., arXiv:1108.3856v1

Conclusion

Reported recent developments of a torsion balance at Seattle University.

Critical investigations on how to understand the relevant contributions in the total force measured from a force-distance experiment even at the minimized electrostatic condition. That is,

Fcas VS. FPatch

The problem is not only ours, but also in many other research fields in physics: GP-B, LISA/LIGO, ion trap/neutral atom exp, and NC-AFM, and perhaps more. This unique problem is likely to bring together scientists from different fields of physics.

Acknowledgements

Special thanks to: Dr. Diego Dalvit

Dr. Roberto OnofrioDr. Cheol Park

Dr. Steve Lamoreaux

• Murdock Charitable Trust• Research Corporation (SI-CCSA)• Startup funds made possible by the College of Science and Engineering at Seattle University• University of Washington NanoTech User Facility (NTUF)• The project is completely to be carried out by undergraduate students and myself: Todd Graveson and Charlie Rackson