1. Qfext07 Leipzig 17 Sep. 2007 Casimir force measurements with quartz tuning fork and AFM Dr. Thorsten Ludwig Binnotec e.V. Bouchéstr. 12, Haus 6 12435 Berlin DrLudwig@thorstenludwig.de

2. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Content Force Sensors for sub nano Newton –Light silicon cantilevers –Quartz tuning forks Experimental setups in Berlin –With commercial AFM –quartz tuning fork Measurements Outlook

3. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Motivation To measure influences of different material and geometries on the Casimir force metal plates

4. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Sub pN Force Measurement AFM –Light silicon cantilever Quartz tuning fork –SNOM –AFM –MFM –Atomic point contact –Gas sensor –Micro gyros

5. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Silicon cantilver

6. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig AFM silicon cantilever Standard commercial AFM force sensor –Calibrated, good quality, ready made –Direct force measurement Disadvantage –Need for laser and optical measuring system –Low k 0,01 N/m, very flexible –Adhesion, catch in –fragile –High cost of AFM

7. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Quartz tuning forks Each minute, more than 2,000 quartz watch crystals are produced at a cost of less than $0,20 apiece Vast amount of scientific literature discussing many aspect of quartz tuning forks as force sensors

8. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Atomic resolution with AFM with quartz tuning forks F Giessibl APL 2000

9. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Measuring principal Driven harmonic oscillator Resonance frequency External force creates a frequency shift Proportional to force gradient Phase shift Much literature available W. H. J. Rensena APPLIED PHYSICS LETTERS VOL 75, NUM (1999) 1640 Dynamic mode AFM

10. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Casimir force measurments Casimir force for flat- sphere geometry Frequency shift

11. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Spring konstant k Spring constant k Young module Smaller tuning forks Low k tuning forks ~2000 N/m Higher frequenzy shift L T W

12. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Cantilever vs. Tuning fork Silicon Cantilever –Advantages absolute force Commercial available –Disadvantages External Optical measuring system needed Very low stiffness Catch in / sticking Adhesion fragile Quartz tuning fork –Advantages Self sensing Easy to operate Low cost High stiffness Small amplitude of oscillation Robust Only electrical equipment needed Low energy dissipation –Disadvantages Proportional to force derivate Oscillating sensor

13. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Atomic force microscope

14. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig AFM with optical microscope

15. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig AFM in vacuum chamber

16. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Full AFM system

17. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Tuning fork set up

18. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Electrical set up Function generator LockIn amplifier Quartz tuning fork Reference signal Computer f scan or PLL Keithley 2000 DMM 6.5 digit

19. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Tuning fork measuring equipment

20. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Tuning fork in vacuum Scan 8 Hz Width 800 mHz At 32764 Hz Q=4 10 5

21. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Frequency plot of tuning fork sensor

22. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Long term stability

23. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Casimir force measurement k = 4680 N/m f = 32756 Hz R = 0,6 mm U = 1 mV

24. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Conclusions Silicon cantilevers and quartz tuning forks are both capable of measuring the Casimir force –Tuning fork set up is more sensitive and cost is 1/3 rd –But AFM is necessary to control surface roughness Great care has to be taken to measure the Casimir force with both systems –Careful and precise sensor preparation to keep sensitivity up –Smooth and clean surfaces –Alignment of surfaces

25. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Outlook Further development of the tuning fork set up –Faster automatic frequency shift detection –More options to built a compact robust sensor –Separate distance masurement Conduct Casimir force measurement under several conditions –Material –Geometries

26. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Thank you for your attention Dr. Thorsten Ludwig New Energy Technologies Binnotec e. V. Bouchéstr. 12, Haus 6,12435 Berlin Tel : +49 171 6280 357 DrLudwig@thorstenludwig.de www.thorstenludwig.de

27. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Casimir force with silicon cantilever 200 um sphere On tip less cantilever K = 30pN/nm

28. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Roughness measurments with AFM

29. Qfext07 Leipzig 17 Sep. 2007 Casimir with tuning fork and AFM Dr. Thorsten Ludwig Calibration